{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Handling time-constant singularities in integrate-and-fire neurons\n",
    "\n",
    "This notebook details how NEST handles the numerical instability of the exact integration propagator matrix $P = e^{A h}$ which arise if $\\tau_m\\approx \\tau_{\\text{syn}}$. For an overview over exact integration of integrate-and-fire neuron subthreshold dynamics, please see [the exact integration documentation](../neurons/exact-integration.rst).\n",
    "\n",
    "We illustrate the approach for neurons with alpha-shaped currents, where the synaptic current is described by two differential equations. For exponential-shaped currents, a similar but simpler treatment applies.\n",
    "\n",
    "The singularity-handling code is implemented in `libnestutil/iaf_propagator.[h,cpp]`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Preparations\n",
    "\n",
    "We use SymPy to allow symbolic analysis of the propagator matrices and their limits."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy as sp\n",
    "from sympy.matrices import zeros\n",
    "\n",
    "sp.init_printing(use_latex=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Introduce formal variables for time constants, capacitance and time step $h$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "tau_m, tau_s, C_m, h = sp.symbols(\"tau_m, tau_s, C_m, h\", positive=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The ODE matrix\n",
    "\n",
    "The following matrix describes the ODE system for synaptic current and membrane potential (bottom row). It applies for singular and non-singular cases. For brevity, we write $\\tau_s$ instead of $\\tau_{\\text{syn}}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}- \\frac{1}{\\tau_{s}} & 0 & 0\\\\1 & - \\frac{1}{\\tau_{s}} & 0\\\\0 & \\frac{1}{C_{m}} & - \\frac{1}{\\tau_{m}}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡-1           ⎤\n",
       "⎢───   0    0 ⎥\n",
       "⎢ τₛ          ⎥\n",
       "⎢             ⎥\n",
       "⎢     -1      ⎥\n",
       "⎢ 1   ───   0 ⎥\n",
       "⎢      τₛ     ⎥\n",
       "⎢             ⎥\n",
       "⎢     1    -1 ⎥\n",
       "⎢ 0   ──   ───⎥\n",
       "⎣     Cₘ    τₘ⎦"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = sp.Matrix([[-1 / tau_s, 0, 0], [1, -1 / tau_s, 0], [0, 1 / C_m, -1 / tau_m]])\n",
    "A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Propagator in the non-singular case ($\\tau_m\\neq \\tau_s$) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}e^{- \\frac{h}{\\tau_{s}}} & 0 & 0\\\\h e^{- \\frac{h}{\\tau_{s}}} & e^{- \\frac{h}{\\tau_{s}}} & 0\\\\\\frac{\\tau_{m} \\tau_{s} \\left(- h \\tau_{m} e^{\\frac{h}{\\tau_{m}}} + h \\tau_{s} e^{\\frac{h}{\\tau_{m}}} - \\tau_{m} \\tau_{s} e^{\\frac{h}{\\tau_{m}}} + \\tau_{m} \\tau_{s} e^{\\frac{h}{\\tau_{s}}}\\right) e^{- \\frac{h}{\\tau_{s}} - \\frac{h}{\\tau_{m}}}}{C_{m} \\left(\\tau_{m}^{2} - 2 \\tau_{m} \\tau_{s} + \\tau_{s}^{2}\\right)} & \\frac{\\tau_{m} \\tau_{s} \\left(- e^{\\frac{h}{\\tau_{m}}} + e^{\\frac{h}{\\tau_{s}}}\\right) e^{- \\frac{h \\left(\\tau_{m} + \\tau_{s}\\right)}{\\tau_{m} \\tau_{s}}}}{C_{m} \\left(\\tau_{m} - \\tau_{s}\\right)} & e^{- \\frac{h}{\\tau_{m}}}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡                               -h                                                                         ⎤\n",
       "⎢                               ───                                                                        ⎥\n",
       "⎢                                τₛ                                                                        ⎥\n",
       "⎢                              ℯ                                                   0                    0  ⎥\n",
       "⎢                                                                                                          ⎥\n",
       "⎢                                -h                                                -h                      ⎥\n",
       "⎢                                ───                                               ───                     ⎥\n",
       "⎢                                 τₛ                                                τₛ                     ⎥\n",
       "⎢                             h⋅ℯ                                                 ℯ                     0  ⎥\n",
       "⎢                                                                                                          ⎥\n",
       "⎢      ⎛        h          h           h           h ⎞    h    h         ⎛   h     h ⎞  -h⋅(τₘ + τₛ)       ⎥\n",
       "⎢      ⎜        ──         ──          ──          ──⎟  - ── - ──        ⎜   ──    ──⎟  ─────────────   -h ⎥\n",
       "⎢      ⎜        τₘ         τₘ          τₘ          τₛ⎟    τₛ   τₘ        ⎜   τₘ    τₛ⎟      τₘ⋅τₛ       ───⎥\n",
       "⎢τₘ⋅τₛ⋅⎝- h⋅τₘ⋅ℯ   + h⋅τₛ⋅ℯ   - τₘ⋅τₛ⋅ℯ   + τₘ⋅τₛ⋅ℯ  ⎠⋅ℯ           τₘ⋅τₛ⋅⎝- ℯ   + ℯ  ⎠⋅ℯ                 τₘ⎥\n",
       "⎢────────────────────────────────────────────────────────────────  ──────────────────────────────────  ℯ   ⎥\n",
       "⎢                       ⎛  2               2⎞                                 Cₘ⋅(τₘ - τₛ)                 ⎥\n",
       "⎣                    Cₘ⋅⎝τₘ  - 2⋅τₘ⋅τₛ + τₛ ⎠                                                              ⎦"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P = sp.simplify(sp.exp(A * h))\n",
    "P"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- The entries in the first two rows of $P$ are unproblematic, as is $P_{33}$.\n",
    "- In the first two entries on the bottom row, $P_{31}$ and $P_{32}$, the denominators will vanish for $\\tau_s\\to\\tau_m$.\n",
    "- $P_{32}$ also appears in the propagator matrix for the case of exponential synaptic currents."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Propagator in the singular case ($\\tau_s = \\tau_m$) \n",
    "\n",
    "In this case, we have"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}- \\frac{1}{\\tau_{m}} & 0 & 0\\\\1 & - \\frac{1}{\\tau_{m}} & 0\\\\0 & \\frac{1}{C_{m}} & - \\frac{1}{\\tau_{m}}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡-1           ⎤\n",
       "⎢───   0    0 ⎥\n",
       "⎢ τₘ          ⎥\n",
       "⎢             ⎥\n",
       "⎢     -1      ⎥\n",
       "⎢ 1   ───   0 ⎥\n",
       "⎢      τₘ     ⎥\n",
       "⎢             ⎥\n",
       "⎢     1    -1 ⎥\n",
       "⎢ 0   ──   ───⎥\n",
       "⎣     Cₘ    τₘ⎦"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A_s = sp.Matrix([[-1 / tau_m, 0, 0], [1, -1 / tau_m, 0], [0, 1 / C_m, -1 / tau_m]])\n",
    "A_s"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and the propagator becomes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}e^{- \\frac{h}{\\tau_{m}}} & 0 & 0\\\\h e^{- \\frac{h}{\\tau_{m}}} & e^{- \\frac{h}{\\tau_{m}}} & 0\\\\\\frac{h^{2} e^{- \\frac{h}{\\tau_{m}}}}{2 C_{m}} & \\frac{h e^{- \\frac{h}{\\tau_{m}}}}{C_{m}} & e^{- \\frac{h}{\\tau_{m}}}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡  -h                 ⎤\n",
       "⎢  ───                ⎥\n",
       "⎢   τₘ                ⎥\n",
       "⎢ ℯ         0      0  ⎥\n",
       "⎢                     ⎥\n",
       "⎢   -h      -h        ⎥\n",
       "⎢   ───     ───       ⎥\n",
       "⎢    τₘ      τₘ       ⎥\n",
       "⎢h⋅ℯ       ℯ       0  ⎥\n",
       "⎢                     ⎥\n",
       "⎢    -h      -h       ⎥\n",
       "⎢    ───     ───   -h ⎥\n",
       "⎢ 2   τₘ      τₘ   ───⎥\n",
       "⎢h ⋅ℯ     h⋅ℯ       τₘ⎥\n",
       "⎢───────  ──────  ℯ   ⎥\n",
       "⎣  2⋅Cₘ     Cₘ        ⎦"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P_s = sp.simplify(sp.exp(A_s * h))\n",
    "P_s"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- This is well-formed and non-singular.\n",
    "- The \"unproblematic\" matrix elements agree with the non-singular case."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Numeric stability of propagator elements\n",
    "\n",
    "We will now show that the matrix elements of the non-singular case converge to those in the general case, so that we have overall\n",
    "$$\n",
    "\\lim_{\\tau_s\\to\\tau_m} P = P_s\\;.\n",
    "$$\n",
    "\n",
    "Using symbolic algebra we find for $\\lim_{\\tau_s\\to\\tau_m} P_{31} = P_{s,31}$:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{h^{2} e^{- \\frac{h}{\\tau_{m}}}}{2 C_{m}}$"
      ],
      "text/plain": [
       "    -h \n",
       "    ───\n",
       " 2   τₘ\n",
       "h ⋅ℯ   \n",
       "───────\n",
       "  2⋅Cₘ "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P_31 = P.row(2).col(0)[0]\n",
    "P_31_l = sp.limit(P_31, tau_s, tau_m)\n",
    "P_31_l"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Test for mathematical equality [as recommended in SymPy](https://docs.sympy.org/dev/tutorials/intro-tutorial/gotchas.html#equals-signs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.simplify(P_31_l - P_s.row(2).col(0)[0]) == 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAD4AAAA2CAYAAACfkiopAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAE20lEQVRoBe2a61EUQRDHD8sAfGSAGSBE4JGBjwiUDKT8BN8szUAyUMkAjcBHBpKBYAb4+w3bW7O3LC7rrOzhddXcvGf6393TMztza2dnZ7NlpP39/ZfyTfx2CP+3hnSaSJ/v8LE1lJdlBr4N6KOhwG8P7TiBfnN4+ImpPyZWCG9IH/fla5k1vgHIT4A9JP5BUBC9aSmBA1bQh8Suc0mNf02pnj9LCRxsajdf3+sKgaDZ96JlBf4AdJ8yhMeAdnvLy7LqdnJtWffxNpSrldReHYndoetHwibhhLxSvbGUA/8Fym0AfyO+kqPokg5j6YTedNVn5Tu0bWxF5IsfKRlzLeZsmXo14RNit4kbSw3nBtjYC3s7iWWVTAM4INwP9ZCa/Y2mhqkDONa3e+Q9gg7Oddpag5TNaK9DfEX4aR6y/W4pwTGOFqiPcB4pKYTyh+fZ4b+5c3NwQUr1uZdJ9PRO/sSKoIqpd+T1B+kERWx/BbEb7f4yvsOYD6u5ZsTFlmANHAZjfT9ngoaHpS4knnBQv05Cq9AS4thonWPkJyrLBhNjh4NV6A1hUveCMjUf1uk85lWU/PrJ+n6BP4rOKQfu+vbYlwOxlVoMBsxLalpSI+lCgPR9whH5Ylpxgoo2GTeZeRQQnxD8OFH48j4jPiX6SOw53qJnhEU8ls9y4GqrAZDOatbwnpBTakv9oNuPfKCe6UULnDG34NR2sgTSalnHHIJXGJ3Wl7x61SnMN+dlh8wv6i+S2pe84Zhp5m/4l2yu9HFS5VVGgLZoTj+F45JoUQJO6VNraJR3tMhOByYcgKBwJDWgabeINr2/kFqdr1DAPGo4V8ii4ly2nR8uYeqaxSJo2XDwMPMHDJSEQJleXmuoqWLEcsPoxHyu+doSyDeWHfm67iJm0j5OI9eCTiGApbbklZia9YpnceCo08FIOrpGm/Piaf42DjDTZHEcrmKNjzP6hEddAZ+wckZhbaXxUcQ64UFXGp+wckZhbW1vb6/4pd4onBYedHWAKSzQyQ+3cm6TV1FhBv9bjcf3eGF5posLv+W9yPBb32/nIO/lDgjrFHhf1rhEjEZjx6MAB4zf6l4zvyZ4/VwDJ/2Y4GWlV0X/5NKCeVpUFDiA1LLXu2rzEfn8aihNTpn3YFqBbS669Untxv4pvcY/w7DPzD4CtEBnYBSOl5it29OszajJYhoHhGbrHXzDtDu4P6H8Q0fdPykuonFAa7aua++1G3fzHSjUdDxKdDQZt7iUxuPGtRcYhKOzu2wpjIua0YtonHHiLr2PtkcH1WeCUsDvORma7OWsaKf3v1YqBVxn1YsArXXoE66VSq1x9+P0xNRD61u0qZcE6XjujT8lzCuJ2M4dQqepT/BlxD8dFPENpYC7lQlAbXa+psC07TzNJSIfJu++bhBY6k98SvB1Jz0FEdvW0+ClT0PU96Iipg5Trm0Z8p8UCqBBlM0JCTSx2gvSN7ifu/+7FeZPWAKthUTav5n08iG0+yMVvYGBcZkVoGs4ALr+1Vzn8ZQ6tf2FOLStID6Tv0uciLRvdFpEvUyqqkFRKVMP5gQbe/pVGHJd59o1/zUGAKyC9C3cc/4G4a/XeRFTDwaHxBUoX1pzMFuMlf+bQUGExQwRbIu1awcOR2pz0XwXywTtR40evsj3+28NeKBtaGrcUgAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$\\displaystyle \\frac{h e^{- \\frac{h}{\\tau_{m}}}}{C_{m}}$"
      ],
      "text/plain": [
       "   -h \n",
       "   ───\n",
       "    τₘ\n",
       "h⋅ℯ   \n",
       "──────\n",
       "  Cₘ  "
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P_32 = P.row(2).col(1)[0]\n",
    "P_32_l = sp.limit(P_32, tau_s, tau_m)\n",
    "P_32_l"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.simplify(P_32_l - P_s.row(2).col(1)[0]) == 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Approximation in the vicinity of the singularity\n",
    "\n",
    "Since the propagator elements converge to the solution for the singular case, we can approximate the matrix elements near the singularity by expanding around $\\tau_m$. We obtain"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{h^{2} e^{- \\frac{h}{\\tau_{m}}}}{2 C_{m}} + \\frac{h^{3} \\left(- \\tau_{m} + \\tau_{s}\\right) e^{- \\frac{h}{\\tau_{m}}}}{3 C_{m} \\tau_{m}^{2}} + O\\left(\\left(- \\tau_{m} + \\tau_{s}\\right)^{2}; \\tau_{s}\\rightarrow \\tau_{m}\\right)$"
      ],
      "text/plain": [
       "    -h                   -h                           \n",
       "    ───                  ───                          \n",
       " 2   τₘ    3              τₘ                          \n",
       "h ⋅ℯ      h ⋅(-τₘ + τₛ)⋅ℯ       ⎛          2         ⎞\n",
       "─────── + ────────────────── + O⎝(-τₘ + τₛ) ; τₛ → τₘ⎠\n",
       "  2⋅Cₘ                2                               \n",
       "               3⋅Cₘ⋅τₘ                                "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P_31.series(x=tau_s, x0=tau_m, n=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\frac{h e^{- \\frac{h}{\\tau_{m}}}}{C_{m}} + \\frac{h^{2} \\left(- \\tau_{m} + \\tau_{s}\\right) e^{- \\frac{h}{\\tau_{m}}}}{2 C_{m} \\tau_{m}^{2}} + O\\left(\\left(- \\tau_{m} + \\tau_{s}\\right)^{2}; \\tau_{s}\\rightarrow \\tau_{m}\\right)$"
      ],
      "text/plain": [
       "   -h                   -h                           \n",
       "   ───                  ───                          \n",
       "    τₘ    2              τₘ                          \n",
       "h⋅ℯ      h ⋅(-τₘ + τₛ)⋅ℯ       ⎛          2         ⎞\n",
       "────── + ────────────────── + O⎝(-τₘ + τₛ) ; τₛ → τₘ⎠\n",
       "  Cₘ                 2                               \n",
       "              2⋅Cₘ⋅τₘ                                "
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P_32.series(x=tau_s, x0=tau_m, n=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We thus have \n",
    "\n",
    "\\begin{align}\n",
    "P_{31} &= P_{s, 31} + \\frac{2h}{3\\tau_m^2}P_{s, 31}(\\tau_s-\\tau_m) + \\mathcal{O}((\\tau_s-\\tau_m)^2)\\\\ \n",
    "P_{32} &= P_{s, 32} + \\frac{h}{2\\tau_m^2}P_{s, 32}(\\tau_s-\\tau_m) + \\mathcal{O}((\\tau_s-\\tau_m)^2)\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Focusing on $P_{32}$ and dropping the quadratic term, we obtain\n",
    "$$\n",
    "\\left|\\frac{P_{32}-P_{s, 32}}{P_{s, 32}}\\right|\\approx \\left|\\frac{h(\\tau_s-\\tau_m)}{2\\tau_m^2}\\right| \\ll 1\n",
    "$$\n",
    "where the inequality follows because $|\\tau_s-\\tau_m|\\ll \\tau_m$ by definition in the near-singular case and $h<\\tau_m$ for all practical purposes.\n",
    "\n",
    "Any violation of this inequality indicates numerical instability in the computation of $P_{32}$.\n",
    "\n",
    "The corresponding inequality for $P_{31}$ is\n",
    "$$\n",
    "\\left|\\frac{P_{31}-P_{s, 31}}{P_{s, 31}}\\right|\\approx \\left|\\frac{2h(\\tau_s-\\tau_m)}{3\\tau_m^2}\\right| \\ll 1\\;.\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Propagators rewritten as expressed in C++ implementation\n",
    "\n",
    "- Implementation uses `expm1(x)` function which returns $e^x-1$.\n",
    "- Show that expressions for $P_{31}$ and $P_{32}$ in implemenation are equivalent to expressions above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left( \\frac{\\tau_{m} \\tau_{s}}{\\tau_{m} - \\tau_{s}}, \\  \\frac{\\tau_{m} \\tau_{s}}{C_{m} \\left(\\tau_{m} - \\tau_{s}\\right)}\\right)$"
      ],
      "text/plain": [
       "⎛ τₘ⋅τₛ      τₘ⋅τₛ    ⎞\n",
       "⎜───────, ────────────⎟\n",
       "⎝τₘ - τₛ  Cₘ⋅(τₘ - τₛ)⎠"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "beta = (tau_m * tau_s) / (tau_m - tau_s)\n",
    "gamma = beta / C_m\n",
    "beta, gamma"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{\\tau_{m} \\tau_{s} \\left(e^{\\frac{h}{\\tau_{s}} - \\frac{h}{\\tau_{m}}} - 1\\right) e^{- \\frac{h}{\\tau_{s}}}}{C_{m} \\left(\\tau_{m} - \\tau_{s}\\right)}$"
      ],
      "text/plain": [
       "      ⎛ h    h     ⎞  -h \n",
       "      ⎜ ── - ──    ⎟  ───\n",
       "      ⎜ τₛ   τₘ    ⎟   τₛ\n",
       "τₘ⋅τₛ⋅⎝ℯ        - 1⎠⋅ℯ   \n",
       "─────────────────────────\n",
       "       Cₘ⋅(τₘ - τₛ)      "
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P_32i = gamma * sp.exp(-h / tau_s) * (sp.exp(h / tau_s - h / tau_m) - 1)\n",
    "P_32i"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.simplify(P_32 - P_32i) == 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{\\tau_{m} \\tau_{s} \\left(- h + \\frac{\\tau_{m} \\tau_{s} \\left(e^{\\frac{h}{\\tau_{s}} - \\frac{h}{\\tau_{m}}} - 1\\right)}{\\tau_{m} - \\tau_{s}}\\right) e^{- \\frac{h}{\\tau_{s}}}}{C_{m} \\left(\\tau_{m} - \\tau_{s}\\right)}$"
      ],
      "text/plain": [
       "      ⎛           ⎛ h    h     ⎞⎞     \n",
       "      ⎜           ⎜ ── - ──    ⎟⎟  -h \n",
       "      ⎜           ⎜ τₛ   τₘ    ⎟⎟  ───\n",
       "      ⎜     τₘ⋅τₛ⋅⎝ℯ        - 1⎠⎟   τₛ\n",
       "τₘ⋅τₛ⋅⎜-h + ────────────────────⎟⋅ℯ   \n",
       "      ⎝           τₘ - τₛ       ⎠     \n",
       "──────────────────────────────────────\n",
       "             Cₘ⋅(τₘ - τₛ)             "
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P_31i = gamma * sp.exp(-h / tau_s) * (beta * (sp.exp(h / tau_s - h / tau_m) - 1) - h)\n",
    "P_31i"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.simplify(P_31 - P_31i) == 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Numerical convergence experiments\n",
    "\n",
    "- Compute propagator elements as implemented in code\n",
    "- Test convergence against singular value for $\\tau_s\\to\\tau_m$\n",
    "- Test for different time steps $h$\n",
    "- Very small time steps $\\mathcal{O}(1 \\mu{s})$ can occur in neurons with precise spike times and are thus relevant\n",
    "- We set $C_m=1$ since it is just a scaling factor "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "              -- N E S T --\n",
      "  Copyright (C) 2004 The NEST Initiative\n",
      "\n",
      " Version: stinebuu_propagator_class@79327cc82\n",
      " Built: Nov 29 2022 17:36:40\n",
      "\n",
      " This program is provided AS IS and comes with\n",
      " NO WARRANTY. See the file LICENSE for details.\n",
      "\n",
      " Problems or suggestions?\n",
      "   Visit https://www.nest-simulator.org\n",
      "\n",
      " Type 'nest.help()' to find out more about NEST.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import nest\n",
    "\n",
    "nest.set_verbosity(\"M_ERROR\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calc_p(tau_m, tau_s, h):\n",
    "    beta = tau_s * tau_m / (tau_m - tau_s)\n",
    "    inv_beta = (tau_m - tau_s) / (tau_s * tau_m)\n",
    "    gamma = beta\n",
    "\n",
    "    p31 = gamma * np.exp(-h / tau_s) * (beta * np.expm1(h * inv_beta) - h)\n",
    "    p31s = 0.5 * h**2 * np.exp(-h / tau_m)\n",
    "\n",
    "    p32 = gamma * np.exp(-h / tau_s) * np.expm1(h * inv_beta)\n",
    "    p32s = h * np.exp(-h / tau_m)\n",
    "\n",
    "    return p31, p31s, p32, p32s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1200x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tau_m = 10.0\n",
    "tau_s = tau_m + np.logspace(-12, 0, 26)\n",
    "h = np.array([[1, 0.1, 0.01, 0.001]]).T\n",
    "p31, p31s, p32, p32s = calc_p(tau_m, tau_s, h)\n",
    "\n",
    "fig = plt.figure(figsize=(12, 4))\n",
    "ax1 = fig.add_subplot(1, 2, 1)\n",
    "ax1.loglog(np.abs(tau_s - tau_m), np.abs(p31 - p31s).T, \"o-\")\n",
    "ax1.set_ylabel(\"$P - P_{singular}$\")\n",
    "ax1.set_ylim([1e-20, 5e-2])\n",
    "ax1.set_xlabel(r\"$\\tau_s - \\tau_m$ [ms]\")\n",
    "ax1.set_title(\"$P_{31}$ difference from singular value\")\n",
    "ax2 = fig.add_subplot(1, 2, 2)\n",
    "ax2.loglog(np.abs(tau_s - tau_m), np.abs(p32 - p32s).T, \"o-\", label=[f\"h = {hv:.3f} ms\" for hv in h[:, 0]])\n",
    "ax2.set_ylim([1e-20, 5e-2])\n",
    "ax2.set_xlabel(r\"$\\tau_s - \\tau_m$ [ms]\")\n",
    "ax2.set_title(\"$P_{32}$ difference from singular value\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- $P_{32}$ shows perfect convergence towards the singular value up to the limits of numerical accuracy\n",
    "    - This holds for all step sizes $h$\n",
    "    - This is plausible because $P_{32}$ contains multiplications only: `gamma * np.exp(-h/tau_s) * np.expm1(h*inv_beta)`\n",
    "    - The only difference is handled internally in `expm1()` and `inv_beta` goes to 0 in the limit\n",
    "    - Thus **no singularity handling is needed for $P_{32}$**.\n",
    "- $P_{31}$ converges only up to a point, which depends on the size of the time step $h$\n",
    "    - Numerical instability occurs for smaller differences in time constants\n",
    "    - Instability occurs earlier for *smaller* time steps\n",
    "    - The instability arises from the difference `beta * np.expm1(h*inv_beta) - h`\n",
    "    - There seems to be no way to reformulate the propagator to avoid this \n",
    "    \n",
    "#### $P_{31}$ instability and membrane time constant"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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k5Tv3nZSjeKjmeq/7vraNUHwUkTkkaCu0TiFxM5Obm4vVaiU+Pt5le3x8PJmZmZqu8f333/PBBx+wZs0aBg0axKBBgzhw4IDq8YsWLaKoqMj55/jx46rHOmr8zWbfPZYFAncc6f5Wq9XHkc3PiG5RJIarGwsS9lS3tqzo35CxLBC0No56dffodWGFdy2Z9jBWfaFlLHcEh6ZA0JbR/E5O+wz+e72r4Q9QnGHfvv4Bxf0B5Vm8ErCCV4wrSCDfZV8C+bxsXMErAStIkNz2Sfm8ErCCybpdqs9eP3NIIPBX2kXk34F7SrQsy5rTpM8++2xsNpvme5lMJkwmbX3O1Z5PINBCa35v9DqJiwd14uXv/vDY114UwhszlgWC1kCLqB903O4bWsayw6GZWVSp+DmKFqWC9kBbFqPT9E62We0RfVX1DmD784r7JWTnVvePRCeBXLvTPTqqA2QkFhv/w4aqYc4SACVE5pDAn2kXxn9MTAx6vd4jyp+dne2RDSAQCLRTUlnDmn0nAAgO0FNWXZd90NEUwgWC1karUFVkcAD5te39QIzV+uh1Eosv7MPfVqV67OsoThJB+6ZDtLE8ut0z4u+BuptUcv6fwj4vQ19CJknKY4TuMD/Y+qgeJzKHBP5MuzD+AwICGDp0KBs2bGDmzJnO7Rs2bOCiiy5qxSdr+4wdO5ZBgwaxYsWK1n4UQSvw1Ne/kFFUSZcoM2vvOIcDJ4raZCRBIGgPaI0mPTC9NwnhQWKsqjClXyIvXzuEJWv207V8v1PQ63jIQB6Y0b/9GEiCDkeHaWNZmtUsl7ECqYEmcvR6Yq1WhlRWofd5FsRRqLhdZA4J2gJtpua/tLSUffv2sW/fPgDS09PZt28fx44dAyAlJYU33niDf//73xw6dIi7776bY8eOMXfu3FZ86ubHapPZ8Ucen+47wY4/8rDafCWAtj0yMjK4+uqrOfPMM9HpdNx1112azjt27BgXXnghwcHBxMTEcMcdd1BdXe1yzIEDBzjvvPMICgqiU6dOPPzww8iy62f43XffMXToUAIDA+nevTuvvPJKc/1qbYq9Rwt454ejACyd2Z+QQAOjTo/mokGdGHV6tKsxYbNC+lY48KH9b9up1ycQCNoTSnO91mhSQniQ+lgVADBFt5vtQXfxfsAjPBfwAu8HPMK2wDuZotvd2o8mEDQKX20swS5G1y7WjSFNz+rdaA5icuckbkqMZ0FcDDclxjO5cxIbzUE+z80mQi1xQGQOCfyeNhP537NnD+PGjXP+nJKSAsANN9zAypUrueKKK8jLy+Phhx8mIyODfv36sXbtWpKTk9Uu2eboEKlc2Nu8xMbGcv/99/PMM89oOsdqtTJ9+nRiY2PZtm0beXl53HDDDciyzPPPPw/Y28VMnDiRcePGsXv3bn799Vdmz55NcHAw99xzD2B3Kk2bNo05c+awatUqvv/+e+bNm0dsbCyXXnppi/3O/oKjTjCjsILlG39BluHSIadxds8Y9XY6vtR2BQJBg1Ca6xPCAxnRNdLreSLqpJFaoTDJzUySHEJhl78j5i5Bm6NDtbFMHm1fZxRnoJreL+lqC/g99280B5ESF+OxJ1uvJyUuhuXZuUwor1C6KIQlMXviVRz94hePz3vm4E7taj0uaJ+0mcj/2LFjkWXZ48/KlSudx8ybN48jR45QVVXF3r17Offcc1vvgZsZNYVnRyrXuoMZLXZvm83G/PnziYqKIiEhgSVLlrTYvQC6du3Ks88+y/XXX094eLimc9avX09aWhqrVq1i8ODBTJgwgaeffprXX3/d2SN29erVVFZWsnLlSvr168cll1zCfffdx/Lly53R/1deeYUuXbqwYsUKevfuzS233MJNN93EU089pXrvzZs3I0kSX3/9NYMHDyYoKIjx48eTnZ3NV199Re/evQkLC+Oqq66ivLzced6HH35I//79CQoKIjo6mgkTJlBWVtaET65prDuYwdnLvuGq138g5X8/8VdBJToJRnWPsi+WV/SDty+Aj262/72in6qarlNtN+2z1vllBII2ire5/rOf6uZ597iSqFfXSD2hMM9PqdYUWLdQZC8J/B737KDM4g7UxlKntwcYAOXZUIJRf1fcb0Xi8ehI+2h3Fwqv/XlZdCRWtdj+lMeZ0v80ti0Yz3tzzuLZKwcx99zuAGw6nE2Rj84rAkFr02aM//aGLMuUV1s0/SmprGHxZz97TeVa8lkaJZU1mq7nnubui7fffpvg4GB27tzJE088wcMPP8yGDRtUj1+9ejUhISFe/6xevbpBz+CLHTt20K9fP5KSkpzbJk+e7HQEOY4577zzXFRkJ0+ezMmTJzly5IjzmEmTJrlce/LkyezZs8fZslGNJUuW8MILL7B9+3aOHz/O5ZdfzooVK3j33Xf58ssv2bBhgzMLISMjg6uuuoqbbrqJQ4cOsXnzZi655JIG/9s0F2oGh02GjR+/gaxo4J+E7c/hVW1XLKIFAs1oUfMPDzLy0tVDSHBrwZkQHth+6nlbEp9CYTIUn7AfJxD4KfWd9Xe+v4+rXv+Bh7/4WdO57UaMrs8Me5ZOmNucF5Zk3z7pX4r7U6OSyDIYVJX9ZEki02AgNSrJdUdghEtWkF4nOcur/jGlF2fEh1BUUcMrCt2RBAJ/os2k/bc3Kmqs9Hnw62a5lgxkFlfSf8l6TcenPTwZc4D2f/oBAwawePFiAHr27MkLL7zApk2bmDhxouLxM2bMYOTIkV6v2dxdGDIzMz2uGRkZSUBAgLMLRGZmJl27dlV8jszMTLp166Z4nfj4eCwWC7m5uSQmqi+sH3nkEcaMGQPAzTffzKJFi/jjjz/o3t3uEZ41axbffvstCxYsICMjA4vFwiWXXOIsTenfv3/jP4AmUN/g0GFjhO6wUwBrj+0MHjS+g6wYJfNFvUV0t3Oa/8EFgnaGFjX/oooaIoMD2LZgfJtt5dWqaBUK83JcW26jJmj7qIn6FZR5D1C0y7KgPjOg13TlksTa/XLPKZSvfQfLyWMYkrqQ0zsOdtzv89JZ0x5nd0kOOWkfEXt8D0POnIpepRxIr5P4x+RezHlnD299n87s0V2JD2snThZBu0MY/wKfDBgwwOXnxMREsrOzVY8PDQ0lNDS0pR/LA0nBiyvLsst292MckfaGHqNE/c8pPj4es9nsNPwd23bt2gXAwIEDOf/88+nfvz+TJ09m0qRJzJo1i8hI7zW9LYHD4Jis28Vi4zskSfnOfblyKDFSSdNu0EyqvAJBe0drOm52SaUz6iRoIFqFwlSO6yjaOwL/REt2ENgNfdntZ2inZUE6vWqAoXj9erKWPoalXivw5NgoRpxjY9eZ3pOfn9jzFAVVBfYfEuOJL9zOwqMbmZA8QfH4Cb3jGJYcyZ6jBSzf8CsXD+okHIQCv0QY/61EkFFP2sOTNR27Kz2f2W/5ViBeeeNwTR7dIKOWRiZ1GI1Gl58lScJms6kev3r1am677Tav13z11Ve55pprGvQc3khISGDnzp0u2woKCqipqXFG8hMSEpxZAA4cTgxfxxgMBqKjvS+0639OkiR5/dz0ej0bNmxg+/btrF+/nueff57777+fnTt30q1bN62/drOQXWI3/F82rvDYF00TDX9oFlVegaA94h5Bjgkx+T6JdpS22xr4FAqzC3qRPNpjT4dpoybwW7RkBwFEBgeQX1bX7SihAzqoitev58Sdd9WK/tWhyy3gno9lnr4Erw4Ap+FfS7ZkI2Xz3Swf+4yiA0CSJBZM7cVlr+zgg93H+WD3cee++g5CkTkkaG2E8d9KSJKkOfX+nJ6xJIYHkllUqbZUISE8kHN6xvrFBNIaaf+jRo3i0UcfJSMjw5mav379ekwmE0OHDnUec99991FdXU1AQIDzmKSkJGc5wKhRo/j8889drr1+/XqGDRvmYcw3FUmSGDNmDGPGjOHBBx8kOTmZTz75xNnJ4lQRF2xksfEdANy/Pj6SHXygvogWCDo6ShHkmOAAdJJda0OJdpm2e6pxCIX993o846O1THm8Lm24Fl9t1CTsbdQm9knwi/ewoH2iNTvogem9SQgP6rAGpmy1krX0MQ/D377Tvm32Bhu7e0rIGj8XWZKQgGW7ljGu8zj0Os9AWl5pleK5Dgfhred247OfMkTmkKBVEYJ/bQC9TmLxhX2AtqHwHBoaSo8ePbz+8VUWsG/fPvbt20dpaSk5OTns27ePtLQ05/5PPvmEXr16OX+eNGkSffr04brrruPHH39k06ZN3HvvvcyZM4ewsDAArr76akwmE7Nnz+bgwYN88sknLF26lJSUFGdK/9y5czl69CgpKSkcOnSIf//737z55pvce++9zfoZ7dy5k6VLl7Jnzx6OHTvGxx9/TE5ODr17927W+3hgs0L6Vjjwof1vm5UR+sMkSfkehn/DUPlmKiyiBYKOjprAZm5ZtVfDH/xrrm+zqAmFGc2qbf4a0kZNIGgu3BX9tWYHJYQHOcXoRp0e3eHmjPI9e11S/d2RgJgS6H3cdcKNNHkvvZSBzPJMUrNTPfY5HIRq58nAq1vSW6Vrl0BQHxH5byNM6ZfIy9cOUez93B49hoMHD3b+9969e3n33XdJTk52qvIXFRXxyy+/OI/R6/V8+eWXzJs3jzFjxhAUFMTVV1/t0qIvPDycDRs2cPvttzNs2DAiIyNJSUlxibR369aNtWvXcvfdd/Piiy+SlJTEc889x6WXXtqsv19YWBhbtmxhxYoVFBcXk5yczNNPP83UqVOb9T4upH1mb3FVX+k6LAkpYYD6OV6pXUyM/j84+KHHdZnyuOiVLRC4oU3R30CQ0eDSuqu9zvWtRq1Q2Mr336Xw52+4y/gxIMHp4xUPb4geg0DQHChlB0WZjUiSckAbRHaQA0tOjqbjokolnhn7DNXWamLNsWSVZbFo2yKf5+WUe15fa0mGOyJzSHCqEcZ/G2JKv0Qm9kk4pbVCmzdv9ti2Zs2aFrufA18t72bPns3s2bNdtnXp0oUvvvjC63n9+/dny5YtXo8577zzSE319OqqMXbsWI/nVXq+JUuWsGTJEgB69+7NunXrNN+jyaR9Vpvm6va5Fp9E57XtVT3MMVCeW/dzfQN/whJ1tV2BQOBEm6K/hZeuHopOJ3XYtN1Tgk5PfswInrNGcm3IbmKqjkPaGhh8rcehWnUW4kIDRU2voMmo6Uvkl6sr+ovsoDoMsbGajuvSbaBL/f7uTN/6WgCxZs/rN8XxVz9zSAi5CloaYfy3MYTCs6DB2Kz2iL9KrFGWaz3Pkmfyvp3a2v079sHxncoGvhe1XYFAUIfWBWJuWRUXDerUwk8jCAk0ABI/hE3lgpzXIPU/isb/iG5RXrV3wK6ZkpZRRMp/94maXkGj0ZIdFBFkIFBkB6liHjYUQ0IClqwsxTQJGcgLhRGTZ7tsHxI3hHhzPNnl2cgK/wKSLBMfnMCQuCEe+5pDiFVkDglOBcL4FwjaO0e3u6bku+Ew+msbGqLYIGjK42AIEAa+QNBA2pyiv83aobJ4Qkx2IdfNQedzgfQGHP8Bcn+DmJ4uxzm0d/62KlVNJhCbDP/64pDHdtENQNAQtGQHFVZYWC2yg1SR9Hri71tkV/t3wzF2P5waxlPJY1326XV6Fo5YSMrmFCQkDweADCzofqmi2J8WB6EvRCcXwalACP4JBO0Nd1G/Em0iMtJZ8zwFsMKSVAWwBAKBd9YdzODsZd9w1es/cOf7+7jq9R+47T97vJ4jYY8Ut0rNbtpnsKIfvH0BfHSz/e8V/ezb2yn2yD/8ZQmHnpPsG3/8j+KxDu2dhHDXBXpieCBPXNofo17Z8HIYAg99noZVTdFRIKilIdlBHVnUzxdhkyYRe889HtvLIgN5+hIdSRdcglHv2cVpQvIElo9dTpw5zmPfmdXVTLAoO0O9iXNrIUCvo1+nMA+RRzFnCJobEfkXCNoTSqJ+geHazj1zGkx6pENF/QSClkKtZre0yur8b5U8m9ap2VXVBcmwb2+nTsBQk30ZVFplgXOuhV/Xwb73YPwDoGAYTOmXyNgz4+j1gF2z5fXrhzK+Vzy70vOpsaov0kVNr0AJJX2IuFA/zw5qQ+jD7d2e0OnAZkPfvSu3XZFBDTrm97hY9bwJyRMY13kcqdmpTnG/+7Yu5BeTid3HvmX4yFsVz1MT504MD2TGwERe25IOKGcOVVttXPLSdoora8gqrnI511HOIfREBM2BMP4FgvaC2uK9sgiwl71JCu8ImwxV5gSCHIa+SO0XCJqEpppds5FAg94/ana96oLUalGvWwi9prc7Z6Aj8l9aaYEzpkBwLJRlw28boNc0xXMqquscOOPOjENfm3qtBVHTK3CgpOafEGaie0yw1/OEor92qg4dBiDk3HMp3byZ6hMnsNhs9I7pw5lRZ3o9V6/TMzxhuPPn1F/W8EH2Dp4tSeM/suxsEe2ON3HuwV0iFR0D156VzPObfuO37FKP6znKhm49txuf/ZShqiciHAMCrQjjXyBoD/gS9XMcJttFqaj3M8BDNdfzKDra17JeIGgdNNXsltew+uYhrVOz617XL9u86oKADMUn7Oe0M+dgSP3Iv94IA6+E7c/bU/9VjP/iSrvienCAHoPeXj3ZkG4AAoFaZlBmcRWZ9aK+fpUd1AapPGTX4AidMpmyH35AX1lJQoGei8+6uMHXum3oHXz65ff8pIfvjqxnbLfJqseqiXOrOQYA/r0tnUpLtcc5jn//V2uzBuqj1TEgENRH1PwLBO0BX6J+2KP+BYS6bM8kmr/V3MX7pYPYlZ7fwg8pEHQM/LpmV6mu/3/Xazu3NKtln60VcBj/JZUW+4bB19n//vVrKFH+fYsr7MeGBdWVBTjEvtT+BVtVy0HgV2jJDIoKDuClqz31JRLCA4VwpEZkm43KX34BIKhfP+TunQHoka1jevfpDb5ebFw/rq60AfDc3mewybZGPZceG6N0aVyk38EoXRp6bOxKzyevzNPw94Vc++fVLekeDmeHY2DdQW26T4KOg4j8CwTtAY2L8odrriOLKOIoJJsIdtl6Yav1AYp0VIGg4SilWkaYPWvFlTjlUWC10qCKQm3nh8Q39xO1Klabld+Lf8IQtg+LJZSK6gkExZ4Jp42Av3bBt0vtmQ5u+ieOyH9oYN0SSks3ABGtFYC2zKD8smoigwPYtmC8SOX2gdVmddbmx5pjGRI3BL1OT/XRo8jl5UgmE/sDc0mPLKU/cE55Z8JNGrWQ3LgprC//qzrEb2UnWPvnWuKD4z3u6xUlXaawJPS9FgCxjXomNWoLtnjo8zQm9kkQ3xuBE2H8CwRtEfe0XZ22oZxFFD/Y+ijuE+moAkHDUKrZjQs1EWT0nlTXKjW7PkqDvCPZO38kj27up2o1Nh7dyOO7HierPIugTvZt09d8yn0jFzEhob/d+E9daf8D9t9/yjLoM4OSWuM/LNDVyaMm9hVo1LHiikEiWisAtDvas0sqVdPHBXbqj2MH8eZ4Fo5YyIhD9kh6eqyN+ZvmMDHERn/A8MdxNh7dyITkCQ2+X3jSUGbv28nzURH88/t/YpXr9D8c91W9rhdR1eG77mKy7k6+to1o8DN5QwiNCpQQxr/AK2PHjmXQoEGsWLGitR9F4EDJc+yjsYwNyJSj2WXr5bFPiAcJBA1HrWY3u8Rerxtg0FFtsflPza6P0iB1ap9xyuPtRuxv49GNpGxO8ejhnVORTcrmu1melYvH8r1e14PiisGAa9q/gyn9EpnYK5bDO7/mxF/p/PunCvZYejHgtIiW+WUEfo97dlBMiFDzbw7UxnF2eTYpm1NYerAPpwO/xVoAPenx9rnstMwabtucwvKxyxvuAEgaTKc9FpDBitVll+O+itfVIKr6UMB/2Fg5DGsLVGSLzE5BfUTNf1vDvYe7zer7nDbId999x9ChQwkMDKR79+688sorPs+58847GTp0KCaTiUGDBikec+DAAc477zyCgoLo1KkTDz/8MLLsOhk35t6nDIfn2GMRr2ReOPbYf36o5jpnir/7kSIdVSDQjiY1/yBj69XsKr0ntNbrB0W6/hyW1K7a/FltVh7f9biHweBEllkWHYHnm7X2+HULKamwL6Trp/07SfsM/XP96bvhaiYdup/3Ax5hS8Ad7Pjyreb6FQRtiHUHMzh72Tdc9foP3Pn+Pq56/Qf+791Ur+56oQ/hG2/jWK79X8nP+wE4Emf/tI/FgU2CiDIIL5VZtmsZ1gauoa2J/XkmKgIlI97xLIrX9anLJJNAHsN1h9Fj4yxdGjN02zlLl4aOxmkL1Ec4ktouVpvMjj/y+HTfCXb8kYfV1pjsPVdE5L8toVIr5EhFbC+kp6czbdo05syZw6pVq/j++++ZN28esbGxXHrpparnybLMTTfdxM6dO9m/f7/H/uLiYiZOnMi4cePYvXs3v/76K7NnzyY4OJh77rmnSfc+JfhM25UgKBLZEIhUUvcdydNFc3/ltewLOYd4cOkf22qtxQSCNoyWmt3skqrWqdlVe08kDtZ2/qyV9gi/o6SoXq17eyA1O9UlRdgdWZLINBhIDTQxvLLKfS8UnyA0ew8Q5pH2r5bWm0A+M39bRNX+REwDZjbL7yHwf9Syg/LLa1TPEQ55bfgaxwBds+yfvCPiX22UOBkFp+VBcpaNn0IySc1OdWnn5/O+5SfJMqibTjIymeWZpGbuZnhVTd08WqJNdO/xPscJ+v1l4slzbssimm097uXeg8m192gY8WEm4UhqoyiVFjZHFwdh/LcVvNQKOVIRW8oBYLPZmD9/Pm+88QYBAQHMnTuXJUuWtMi9AF555RW6dOniLDXo3bs3e/bs4amnnvJqgD/33HMA5OTkKBr/q1evprKykpUrV2IymejXrx+//vory5cvJyUlBUmSGnXvzZs3M27cONatW8fChQs5fPgwo0aN4v3332fv3r2kpKRw4sQJpk+fzptvvonZbAbgww8/5KGHHuL333/HbDYzePBgPv30U4KDVXr8nvzRdzuuinz+blhCXrXFRdQvwGDgyzln0TU6WIgHCQRNxG9rdlXfEyc1pPzX1vV3O6ddGfvu5JTnaDtOr/4Z6EpOcpbuL0aU/Q7pBXVaCCrOWZ1kb6tqWbsQU78Zqp+v6NPdftCWHWQg0Gggs7huPhEOeW34GscRpTIRZfZI/7G4uu1H4yROy5PplgU/na59PtB6X+dxH98EuSfqNgRGqh9cj66/v+3xnYkjn0t/v4/u455lXuppHobgjIGJvFbbBlDp+6aTJIoqaggPMor5pQ2h2g60totDUzIIhfHfWsgy1JRrO9Zmha/m461WiHULoPtYbYs2o9ne900jb7/9NikpKezcuZMdO3Ywe/ZsxowZw8SJExWPX716NbfddpvXa7766qtcc801ivt27NjBpEmTXLZNnjyZN998k5qaGoxGbUraStc977zzMJnq6u0mT57MokWLOHLkCN26dWvSvZcsWcILL7yA2Wzm8ssv5/LLL8dkMvHuu+9SWlrKzJkzef7551mwYAEZGRlcddVVPPHEE8ycOZOSkhK2bt1aV4Igy1BdCtYasMj2n8vzVO9dH315Lj/YXIW5Ki02fssq4fTYECH6IhA0kDZRs6tF0M8QBBbHwlGhVKgd1fWrEWvWpqgda1VPB57813PMCiiE37D/CUuCIbO9Olh0EgRXZmI78j267ud67NcS4RHOgbaDluygwgoLq68eik4niX/TBuJrHHfLtM9vJ6PsEX8HR+IlxhyS6Zota7pOQ+/rILo0l92BJnL0emKtVoZUFqB1ZnX/15dq1/mDf17Gtn/sZ9fRIo/vy+AukYris1UWKxlFlVz0wjaqrTaXzM/miCALWgZvzsPm6OIgjP/WoqYcliY108Vk+6Lj8c7aDr/vJASoRJcVGDBgAIsXLwagZ8+evPDCC2zatEnV+J8xYwYjR470es34ePWWUZmZmR774+PjsVgs5ObmkpjYuIkqMzOTrl27Kj5HZmYm3bp1a9K9H3nkEcaMGQPAzTffzKJFi/jjjz/o3r07ALNmzeLbb791Gv8Wi4VLLrmE5GR7Klf//v3tF6oohKK/wFabGmiRoaQA/vhI0++ZTYTHNtHu5dQgFuftDyWjLEyp1rserSKiqUXQz1IBY++zK9h7lI893q7Kx9QYEjeEeHM82eXZivXCkiwTb7UyxCPlv44Qa6HrhuIM2LxU0/0P/fYbfd2Mfy0RHqBF0j8FLYPW7KDcsiouGtSphZ+m/eFrHHfNtv99JN71/Zteu7zrmiWTYE5gSNyQht83IJzsqkJkpSCaLGOSZe6LjSa7XnlAvMXCwrwCJpRXgKIMrK9kfnvJkf74Dkadfo7H3in9EpnYJ8Fj/ZGeW8bMl77neEGFxznNEUEWtAy+nIdN7eIgjP96GAwG+vXrB8CwYcN44403WvmJ/IMBAwa4/JyYmEh2drbq8aGhoYSGhjbpnpLbpOqIiLtvb4nrNvbe9T+n+Ph4zGaz0/B3bNu1axcAAwcO5Pzzz6d///5MnjyZSZMmMWvWLCIDJShI97y4zQInU73e3yZDJsqK/qLdS8vTUrVZgtZDzSgrrrQ4/9tv1Py1CvpFnw53HXRtFdrO6vq9odfpWThiISmbU5CQPAwHWZJYkFeI3suC3AakukT1qjRH9db8ZqXv5LqftUR4Fn58gKLymhZJ/xQ0D20iO6gd4W0cS0h0q633PxIvuew/WusMSMiHhf3vQt/AeU+v07Nw8F2k/LAESZY9HQCSRJUkke22PVuvJyUuhuXZuUwgGMpz63aGJUGfi+CHl3w/gJd5XqnErFtMMCaDjhKF45sjgixoGRpSWtgYhPFfj4iICPbt23dqbmY02yPwWji6HVbP8n3cNR9q68NsNGu7r+Nwt1R3SZKw2dTVR5ua9p+QkEBmZqbLtuzsbAwGA9HRjTdc1a4LdRkATbl3/c9JkiSvn5ter2fDhg1s376d9evX8/zzz3P//fez84t36HaaelYEAcFQ7SgXqXvZybULVSVFf5ffRbR7aRFasjZL0Dpoqtk1Gwk06FunZtdmdTXgzTHazguJtxv63TyjRx2FCckTWD52uUd/cIBIUyQjpzwAGxe7ZkeYY6A8l43mIB6PjnQR/XKN6ikjI5EhR/HmX4n03H0ck1FHXGggNln2GeEpVBGIE4t3/0DJ8Ws2em+mJVrsNh21cRxvjmdYcRWQw5RJf2OnZY1zf1GwRFGojvASG6MqGpd9O6HXLJZveIDHzbjOA4ZQSqqLKJckj9JaWZKQZJll0ZGMG7YYfVgnV+fr0e3ajP8QL+tDBXal55NbWq26XwSG/AN356FBY6Czsc5DYfy3FpKkPfX+9PF2z2BxBsqRiFqhptPH+0X0pqlp/6NGjeLzzz932bZ+/XqGDRvW6Hp/x3Xvu+8+qqurCQgIcF43KSnJWQ7QUvdWQpIkxowZw5gxY3jwwQdJTu7CJ19uIOW2a9VPqi5TTNutNidwR+EVfG0b4fWeIsrQ/LR0bZagddBUs1tew+qbh5z6ml0lRX+Dr7Fd+57Q4iDuAExInsC4zuNIzU7lrR9+4usDhUQnr6WgKod/Fexh2Z0HkI7tcFHr3rjuDlLiYjzGuktUTzGt1163+5/wudiydcz/qE6QNiKoae8VsXhvXdQcv+U1dQESv8kOaofUH8c55TnEmmMZaD6DPx44C4BRY6/h6/C/ueyP2/Y65Vu3UnX4MObBGruguN83ZhDjfllL6rn/R07X0cSaY7Ge3MecA8+pnuPsJGIrY7i78zV5tI91PhDWyfv87e4QTh7d4hFkQdNRch76mhWa6jz07pr0I7Zs2cKFF15IUlISkiSxZs0aj2NeeuklunXrRmBgIEOHDmXr1q0NukdxcTFDhw7l7LPP5rvvvmumJ28GdHp7Oz9ASQoE8CuhptDQUHr06OH1j7eygLlz53L06FFSUlI4dOgQ//73v3nzzTe59957ncd88skn9Orlmt7++++/s2/fPjIzM6moqGDfvn3s27eP6mq71/Pqq6/GZDIxe/ZsDh48yCeffMLSpUudSv9a790c7Ny5k6VLl7Jnzx6OHTvGxx9/TE5OLr17dvN9cvTpWO84wM8T32XPsCf5eeK7/DjzO9Z7MfxF3+CWoyG1WYK2Q0NqdkedHs1Fgzox6vToU2P4//d6z/p+S/3n9f/3hD+g1+kZnjCcAZHjsJb1pn/A7eglPV8d+Yo1f37O7qBA1gab2R0USHVwLI9HR9qX5QpRPYBl0ZFYz1uINSyR3YEm+7mBJhzSgb/keuoIFFaot31rCGLxfurRmh0UH+bqmEsIDxTZYM2IYxxP6z6N4QnDsfz2OwCGhAQMkZEe+4N69wagMu1Q42+aOAg9MLww23nd/NA4n6cB5IQpBL+8rvNrGf+A+vyd9hms6AdvXwAf3Wz/e0U/ehVs1vRMIjDUOjich+5rSCVnofvPTXEetpnIf1lZGQMHDuTGG29UbLn2wQcfcNddd/HSSy8xZswYXn31VaZOnUpaWhpdunQBYOjQoVRVeb58HdHfI0eOkJSUxMGDB5k+fToHDhwgLCysxX83TfSZYW/np9S/uZ0JNXXr1o21a9dy99138+KLL5KUlMRzzz3n8u9eVFTEL7/84nLeLbfc4uK0GVzr0U1PT6dr166Eh4ezYcMGbr/9doYNG0ZkZCQpKSmkpKQ06N7NQVhYGFu2bGHFimcoLi4huUtnnl72KFPHj/F57q4cA3d+8R0ZRQB2oSCJPc7JQkQZTi3Cs94+cE+7izIHaDrP7xT9g6LAGNju3xPNSYjJvhQy1CQzb9A8nv/xeR7c/qDLMZGmSAq89feujeq9HhHOh507kVVeLx1YF8jCjOMsk19jWtVjnK7LcGnF6q1USyti8X7q8evsoA6Mw6gPdAsQOQjsbd9eefhw42+SVJsxcGQ7HPgQQuKI3f8/TafGBqtkvqqt8yU9yFb4ZS0MvNKzW5eXVuBnfHc7V4b8gw9KB6m+NURgqHXw5TyUgPAWKi2UZGdvsbaDJEl88sknXHzxxc5tI0eOZMiQIbz88svObb179+biiy/msccea/A9pk6dyr/+9S+GDRumuL+qqsrFkVBcXEznzp0pKirycBhUVlaSnp7uzEpoEgppPSKS0wZxV/QH0Bnswn5uVFpk0k/k0O37e5Gt1fQreAqrymLxpjFd+epgpt+KzhUXFxMeHq44TlqLhoxlJXb8kcdVr/8AgA4bI3SHFRf27805ixHdokQ3AD9EKe0uQC9RbVV/PTrS7rYtGH/q/g3Tt9ojOr647lP7e6EF3xPtaSx/uu8Ed76/jzE9orlhQjH3fHdP8z+cLPNMdi5nl1kIlOrm/ZNyFA/VXK9YsuVw5EaYjYqCf45jTvn3UADUfW988eyVg/xa0d/fxnJT38kn77ufoo8/Jmbe34i94w6P/dVHjvDHlKlIJhNn7t2D5MWpp0rqf+Czv7tssgKTOyeRbTCoGnRRgVF8c9k33oUG3df5BhO8Nc2+XpyyDOL71u3rPBKeG+il04tERVA8/QqewoZO8bkev6Q/V47oouGXFjQn9deO3lh980hNzsOGjOM2E/n3RnV1NXv37mXhwoUu2ydNmsT27ds1XaOgoACz2YzJZOKvv/4iLS3NRandnccee4yHHnqoSc/dKDq4UFO7oKJQXdHfCzLwUM31qoa/BHx1MJPv/jGOvUcLhIGpkQaPZbcX84jkUSSGBzKwZAsPGt8hSapL73cs7L/Tn0VmUQVnL/vGbx0zHRW1mt36hr/fZNNoVfQvz4X+GkRi2xmNfS87Iv8lldU8sfuJ5n6sWiS72Fe56yI9gXxeNq7gbzV3sdM0xqUMwBHhAfjbqlTF/gMyIqvrVKDUxjXUpG0JLbIyGkZT19eVh+2Rf1Nter87xi5dkMxm5PJyqo8cwdSjR8NukPYZfPZ/Hpv1wMK8AlLiYxU7iQCUW8r5rfA3SqpLnBoEQ+KGuDoDlNb5Ex+GrxfVZn7VwxwN5XleHlYmqCKT9yZZuXOn2WX9YdBJWGwy7+0+zoUDk9j/V5FYN7YQSvNHa7YDbRfGf25uLlarVbE/u7tyuxqHDh3itttuQ6fTIUkSzz77LFFR6mkwixYtckkXd3gmBQKvyLI94u8NSQ+SziMr4MjwB3n/K/VODY7a8r1HC4TwUwNo0FhWEFrThyWxOnkqXX950+Pw+gv7u//r2SFDdANoXfxa0V8py6tco25EAxWh2wuNfS87jP982y8UlWt0sDQUCbvYV6CJ4ZV1UU2dZG/Tutj4H9KvnIfOYFBcgL987RCP7BSA+FATY8/UVmssaBxKmUGxIQEe2dfutKqifxvOEm3K+lqurqaqtuY/UMX4l3Q6As88k4off6Ty0OGGGf8+Sq8mlFeyvMTK4/FJHh0IggxBHCk+whWfX4ENm8u+hSMWMiF5AgBWm9VFoHBI3BD04SrGn1fDv44RsRa2LRjvYoAmhAUy8+Xv+el4IcMe2UBFPZFKEZhoPtTaQA/oFK7p/JZwHrYL49+BUn92rX3hR48ezYEDBzTfy2QyYTJp6+MqEDipLnU16pWQrRDZzb5ysNaARYbSQP4M6AEc9HmL1qgtV3xZtZGFhuaxrFpXd5LuxW8iS57CLDqpNjJn/A8bquwlRO5lATI60Q2glfDbml0lNf/AcKhU6tZcn46t6N/Y93JIoH0pVG4p0HS8LLuW3apF+ZTI0XvOizoJksgj3vgL+u7nKp43pV8iE/skOBfvwSYDiz7aT1ZJFc9s+JVF05QNHUHTUMsMyqltn2YO0FNebfWf7CBQnj/Ckuwp421A96Mp6+uqP/+Emhp0oaEYO6lHSwN797Ib/4cPEX6hhlIqB0e3e0mxB5CZkHuCcdNeJtVsdlkTffnnl9z//f0uhj9Adnk2KZtTWD52OYBi68KFWSeZoP0pPQmJR6+TPAJDs0d1ZcWm31wMfxCBieZCbf7IKKr0ufZoSedhuzD+Y2Ji0Ov1iv3ZvbWUEwhOOVZtys6yrYYyXRgWTFjlamQkwgJbN8VQzcDfeHSj8suqnie7zaNBaE1teScBSVIet+vXcJXhG8WygK+LRohWXa1Aa6bdqaLmZKossv8d3QPy/qjdqGBuCEX/BhNqsrfbq6wMRssnJ1uDkQxlzp/jzfFc2vNSXvzpRZ/nxlqtqvv0Zdlez3VfvMuXDGDOO3t4feufTOqbQLXFJtJ2mxEtmUGhgQaemjWQf33pGtk7JdlBSngRf+O/19sF5dqAA6Cx1Bf78xb8M9WKAVYdaqDon8bSK31ZDsO715VeWW1WnvtRuQ2gjIyExEPbH6KousjDkZhdnkVKiI7l5UGMK68gNdBEjl5PrNXKkMoqH3OWukPYapP5YM9xlWcSbYqbipb5I9Cgo8pid7ycSudhuzD+AwICGDp0KBs2bGDmzJnO7Rs2bOCiiy5qxScTdGhk2R7pt9aA3ggBIfa/NXCsqIYia6n9MpZq8ooree3HHK/ntKSXUM3An9ZtGit/XqnwsqrzZLcLB0A9b78VGvjytZNi+NDjJVC/LCC7ZFAzP7SgPko1d1r1bk9Zza4WNf+aCrhspb3+Uyj6NwvOyH9xF3r0jCe7PFsxki8hEWqM4cShOxl0RiG3jo11OkIBPvztQ/VzZZn42vlC/UF8BCvcUrkn9hrNRYOS+HTfSa54dQcWW919Rdpu09GSGZRVXEVkcIBHSnWrOF+8zh+15ty6hdBrert1EFYeqjX++3jPhAns3cd5fEOyhDWXVLkdl5qd6rJ+ckdGprC6UGVfrSEeE8XjskxWPYHCeIuFhXkFTCivUL2ymkO4IW2KRWCi4WiZPyotNu6ecAbv7z52Sp2Hbcb4Ly0t5ffff3f+nJ6ezr59+4iKiqJLly6kpKRw3XXXMWzYMEaNGsVrr73GsWPHmDt3bis+taDDoqjmb4SAYK+nyUCNbKDY5pryZrXJHM8vx6iTqLHJLZZiqBTd//b4t6RsTvFY0GaVZ/HWz2+p/B52T/ayXcsY13lcmykBUKXW27/RHMTj0ZENfPnW4f5PU7/e92jw7c36yII6lGruoswBlFd7z8Q55TW7PlNKgeITdpGnuw622ZpefyPY5PjcdNwx8F7+uWO+Ryq/VDvLjo25hdUY6GTqz7TuQ1yus3DEQlI2p6icK7Mgr1DFUaihXEMllfuKnv/gU+JdDH8QabvNQUPauCqlVJ9yNKSkU3zCflw7FY6uOuRd7M+BqWcP0OuxFhRgyc7GqDVLOHm0fawWZ6DsZFEeyznl3oM3vpAliUK93h5Uqke2Xk9KXAzLs3OZQLBd7LU+ASFw+jjFazbk+63kPBfZAN7R+vl2jTGfcudhmzH+9+zZw7hxdV9ghxjIDTfcwMqVK7niiivIy8vj4YcfJiMjg379+rF27VqSk5Nb65EFHRVVNf8aqCxUPc0xpWfIUapxvwhzAA/N6NsiKYZK0f24oDiqbFWa61nrIyOTWZ5JanYqwxOGN/q5/IKQeDaag0iJi/H4JFxevgoOAIfXXi2w4Kz31R8GhHBXc6NWc5dfbq/ZjQsNILukunVqdt1FuUoytJ1XmiU6vzQjJoOeAIOOaouNIbHnsnzscsVMpwUjFnDo92TgV8KCPJdPE5InKJ4bGxTLoqQJTDiyDNXeEd7KNVRSueXiDEbtvZvJurs8WgW6p+0CYvHuA3cDJyZEW92536j5a+0GovW4NoZss1F52J7Gryb250AXGIipezeqfvudykOHtBv/Or1dO+G/19OQsRxrjtV2fV+4a5tJEpIssywmhnHX7kZ/Yo/939ccA1+mQP4fsPMVOPcfHpfS+r39NatEdCrSQFPmj1PtPGwzxv/YsWN9pmjOmzePefPmnaInEggU0KrmH9EZik64ZAbIOiPHLZEUoZ4dkFPaMimGG49uVIzuZ1d4r0HVQlM93v6AtfNIHo+pNfzVXr7RkYwtr8TgthiQNDpOfNX7ChqOlpo7nU7HS1cPOfU1u0qR3CCNGQYdVM2/JQkLNJBbWk1plYUJyRMY13mcosbJzoNpAIQGKpdw1T930dZFZJVnkTIshQndp0NUX89/c3M0XPCMermGl1RuCdmZObShahg2tzawjrTdF7753SOtVCzeXVHKDgox+aymbj01f/B0HgZrNDDb6fxRc+IEttJSJKMRk5dW3Q5MvXpT9dvvVB0+TOjYsdpv1GeGXTtBUVRRufRqSNwQ4s3qJUVNQZYkMvWQmn+Q4fUdwuPug49uhu3Pw/A5EBThct6IblEkhgeSWVTp9Yle/PYPj20is8gVpfkjLjTA2U5RidacP9qM8S8QtAm0qvnrDBDf10UToNgaQFG+79TxpqQYKqX1g11dtrlfSA6azePdiqTm/kSWXt25IksSmQYD20PjObeknvBoWBIMuQE2L/V9k3a6IGtNtNTcZRZVnvqaXTVRrgpfrfw6tpp/SxJiqjX+Ky0A6HV6xYylktr93gRYHedO6zaNt35+i+0ntzO9+3S7UdBrut1g2/Qw/LULht3kXafBRyq3I3NohO4wP9j6KB7zzMZfPbaJxXsdatlBpVV14ox+peYPys7D4Dh7cEFWE5Vs3/OHQ+zP1LMnktG3vlJgr14Uf/45lQ0V/QPXsayh9Eqv03stC5KRCTeFU1xV3Oi1mEegpe8lsPVpyE6DHS/C+Pvdnkli8YV9+NuqVMXvt0xdaaI7QhCwDrX5I7ukWvWc1p4/hPEv8MrYsWMZNGgQK1asaO1HaRtoVPPHWmOPIJtCnZsMtYtKXzQ2xVBNtG9Wz1lehWgai4REvDne6WBoy2jNXvio5z946YcCLj5dz5Xjh9ctslJXNrhGUNB0/LJmV4uoH9Co9HBBo3GI/pVUeZ+Hiyvtc3xYkG/j4uxOZ/PWz2+x7cQ2bLINnaSrK9cYfK3d+D+yzftFNKZox1Go6TgHYvFuR0t2UITZSKBBT2axH6j5g7rz0Gv2WPufPyoP1xr/PsT+HDhEAR3nNZgGll6plQU5SooAReeAVjwCLTqdPfr/wbXww0swci4Eu77jpvRL5OVrh3hErRPCA7lyeGee2fib6v0cmUU//JF3alvh+hFaO4IEBxj8Z/5AGP9tjrbcT70hfPfdd6SkpPDzzz+TlJTE/PnzfYo3Hjt2jNtvv51vvvmGoKAgrr76ap566ikCAgIAqKysZO7cuezdu5dDhw5xwQUXsGbNmqbd213RX6OaP3ojsixTVmXFYrNh0Okw6CWfk35iI1OEVNP6y7M1tafyhZo41oIRC9rF91Nr9kJNdQi7A8uJjDJzelAgQ7B7/NVrBMGbGq+gYbjX3EUHB2g675TW7GoR9QN7Onh98Sah5t+ihJjsy6FSH07Y4gr7/lANrVcHxw3GbDCTX5nPofxD9I3uW7ez27n2v//aDdVl6mKwGjOCsonQdFx9hJq3tuygwvIaVt88xD8MHC3Ow8AICDB3uG4gVc42f9qMf0e7v5qjx7CWlqIPCWmxZ3PgraQIUHYOBMVTaav0mhVgNpgZED2A3Zm7Xa/b6wJIHAgZP8G25XDGFI9MhSn9EpnYJ8Ej8+2L/RreU8Dt76ZSWFEX+OpIJUVa5o+SSguvXDPUP+aPWoTx34boEP3UsXdymDZtGnPmzGHVqlV8//33zJs3j9jYWC699FLFc6xWK9OnTyc2NpZt27aRl5fHDTfcgCzLPP/8885jgoKCuOOOO/joo4+afm9FRX8NQ0pnpMhq4mRmCTVWm5aPpEkpQlabVTWtvymp/g4Df3bf2axNX6voyW4v30st9Xo6dOwsexFzciHbimHb1/XGp1qNINi7QET5rk8UeEep5i7QoPNyRivV3GkV25ryGIQmCjX/FkS2WinfsxdLTg69MvPZJUdQWhv5r7/PEBuLedhQJL2eksoadLKNmN8PUnTiJ5d97hj1Rs5KPItvjn/Dtr+2uRr/kV0hvDMUHYdjP0CP85Uf0oe6uIxEhhzFblsvl+1KbkY1tGbItEe0/u65ZVVcNKhTCz+NBrQ4DysL4bK37fNFB5g/HGO1/McfATD1OlPTeYbISPTx8Vizssh/6y3MI0a6jGW1OcD9vkr7ve3TydDnqIwlR8YQK6OrF1tQcw44ui6pBYjKLeWc899zqLDUlY461x/j/gnvXgY7XrD/cRCWZA9M9JmhmPmm1Sle3/CHjlVS1Obmj1qE8d9G8Ba5bel+6jabjfnz5/PGG28QEBDA3LlzWbJkSYvcC+CVV16hS5cuzlKD3r17s2fPHp566ilV43/9+vWkpaVx/PhxkpKSAHj66aeZPXs2jz76KGFhYQQHB/Pyyy8D8P3331NYWNj4e9dT9N+8fQ/jLruVdatfYOHS5zn8xxFGDenP+y8/zt79h0h56GlOZOYw/fyzefPpByGmM0fzy9nw5ae88swyjh9JJzAoiF79BrDizdV0jo2kuNLi4hjQ6ySWXNiHiY2YSH31l/WFhER4QDgmg0nVwL9zyJ3tOiPFW72eAxs2quXCOk8NbuOztkZww7pP+Hzbj3TunMw/QtfD7xvgf7Phlk2Qub9DLNaaG7Wau0pL3RhqtZrdxopyhSYKNf8WpHj9erKWPoYl067RcQUwPjCc3MTbKS6Md9kHYEhIIP6+RXQ/9DP3fP8BMZ8WcdJtX9ikSR73Ofu0s+3G/4lt3DbwtrodkmSP/u9bDelboMf56pl9U5bBf69T/D0kIGv0YuJSzQ1O23XgN2r1pwD37KBwDeUb4EefkVbnYXku9J/Vss/iB7iPY4CTKfcQ/8/7Fcej+7m22nVg7osvwYsvOccyoDoHhE2apHhfLef6ui4oOwfUSgYSzAmcHnE635/83sXwh3rrj9OvRNE6KM6wZyRe/o5iRohWQUB32nNJUZvvCFKLMP5bCVmWPQaqGlablcd2PeY1cvv4rscZmTBSk8EVZAhCUus7psDbb79NSkoKO3fuZMeOHcyePZsxY8YwceJExeNXr17NbbfdprjPwauvvso111yjuG/Hjh1Mcpu0J0+ezJtvvklNTQ1GBSGXHTt20K9fP6fh7zinqqqKvXv3urSJ9Iame6so+i95+lVeeHQB5qBALp+7kMvnLsQUYODdF5dSWlbOzJvv5bn31nPRzf3IyTrJwr/fwl33PcT4KRdQXlpC6q4dIMsUV1o4MyGU8tqSAGuNAWN5IN27a2sD576AzCrTbvirpe8vHr3Ya6qamjhWe0K1Xi8onnJrOSXVJS6GP9jHp4TEsl3LGNd5HHqdHl23c/hsSxD9LeH8Y+al8MrZkPcbLD8TaurNCfW88gJ1/LpmV1HRPxrvcVmhAdHSFK9fz4k77/LomR1dWUTMK0s5oXCOJSuLE3fcyRy1fXfeBc+u8DA4zk46G4D9ufspqioi3BRet7Oe8e81s6/PDIjuAXm/e968+1gGT76BbRM9+3ADvL/7uOrivdXV6k8xStlBPpKDWv8zEor+qqiNY0tOjup49Hlu7ThXwjHOK266kfx/v9Xwc31cl2dXAOrOgQmTJnmswwbGDGTaJ9MUr+tcf/z6LuMAT+ug1kxft9AuXuhmP3gTBPRFe9QDUJo/IhRavtan1ecPFYTx30pUWCoY+e7IZrteVnkWo9/XtljcefVOzEaz5msPGDCAxYsXA9CzZ09eeOEFNm3apGr8z5gxg5Ejvf9u8V56qmZmZnrsj4+Px2KxkJubS2Ki52Jd6ZzIyEgCAgLIrDeJ+kLTvVUU/R+ZP48xwwcBcPOVF7Hosef5I+0nuiefBnojsy7bxaYtO5g220ZudhYWi4Xzp15A0mldAOjZ254SWmO1UV5ldQpQVVbaVHvEu6O0gIw0RWo69/ZBt/Phrx96Td9v7wa+L5RS8qw2K3M2KJkEdmRkMsszSc1OZXjCcOLD7B7gzOJKu/jOsJvg20dcDX/w6ZUX2PHbml1VRf+8ej8IUb9TjWy1krX0MY+FO4AOLwtcub5TVGGfJJG19DFCz7en7ztSfsNiY+kR2p3fS/5kx8kdTOk2pe68rvbMjo1Fh0nZfLenWrQjcjfiASY4DP/L3gabBcpy7Y6l9O8gKw19fB/Fun1vi3eZVlSrP8WoZQfVSw5qG4r+hiAfJ3UM56G3cew+Ht1Lcnyeq3pT+778t1Y2+lzVfZJExoOLsRUVKTsV6jkz6q/Ddmfu9prZKSOTqZdIDTQxpLKK1EATOXo9sVYrQyqr0CND8Qm7g0kh00xNEDAiyOiR7q9Ee9EDUJs/CivUNWJaff7wgjD+BT4ZMGCAy8+JiYlkZ6uryoaGhhIaGqq6XwvumQly7WToLWNBaZ8syw3KctB0bxVF/wF9znD+d3xsFGazme696z67+IQEduzcBcAZffox8uzzmDXxbEafN55R545j4rSLCIuIAMBi06YFUB+10pCCqgKv5zlU+ef0n8Oc/nPadfp+c+Ce5bD2z7WaznN0DEgItxv/uaVV9mySvf9WOcO7V15gxy9r7rSIcgVFgjGow4lytTble/a6RNXc8fW2UN0vy1gyM8l95VUK//c/l3s8EBXMi2NtbD19q6vxH94Ja/TpPG6uUPymOCN3qcvtkbvThkPfi+sOOPo9HPoM1v8TrvtY8bHUFu9gb1c4qnuMj9+47ePX2UFqqDkPXTJGO67z0Nc4dozH8j17CR45omHn+qIR6zOfyLKzBEFpn5ozQ2snom/MQSyKjSbLUGf2xVssLMwrYEJ5hddyEiVBQJssc80bO33etz3oAbTJ+cMHwvhvJYIMQey82vfAAdibtZd5m+b5PO6l819iaPxQTfduCO5p9pIkYfMy+TU17T8hIcEjWp+dnY3BYCA6WlmROCEhgZ07XT/PgoICampqvGYZaLp3Vpb93kESVJWoKvob602qEhJGo5HSSotTzR/AWvu56fV6Xn33E/bt2cmOLd/y3luv8fwTj7Dqs42c1iXZebxWvIn6eUNJlb+jR/cbitZOAI7joswBGPUSNVaZosPfEeNVvMm7V74j4l5zZ9RrGyt+p+hfUQCzVnYYUS5/wZKjbbHcWHJrBWbrE5hfxj0fw2vGTdjG/Mve8q+W1NP6k1Wcqno9GZlMSympgSaG977QdefEh+CXr+CPTfDbRuiprPvjvniPMBtZ8tnPpOeW868v03jqsoGN+2XbCH6bHaSGJudhFBgDO6zzUOs4VjqupeeAFqHWmVG2azeSTucUEow9TVuXjlVhngG5bL2elLgYlmfnMsFHmYi7IKDVJncYPYA2N39oQBj/rYQkSZpT70cnjfaqNO6I3I5OGu0XUdqmpv2PGjWKzz//3GXb+vXrGTZsmGK9v+OcRx99lIyMDGdZwPr16zGZTAwd6tshonrvikLWf/oBwwb0xlh2EsoAyfdnbJP02GSZP3NLndtySqqw1BPxkySJwcPPYvDws7jtrvlMOWsA36z7gpv/9n8Emxr276hV1C/SFOmSCdDeVPlbA0cnAG+ff6gxlCFxQ5x6DJGxP5NXbKIwJwRNcTcfIk/uBrE/v3SaglLNnZZIrd8q+vuhKFd7bydriNVYM92MSIANuHRtEYdv/5k+cf2d+3Kiu4MX4995nF4PvS5w3RjVHUbeZlfw/vp+e7eZ8lxFR5L74v2pywzMemUHH+79i2n9EggKMLTb+cMvs4O8ocl5mA+zPu2wzkOt41jpuNaYA5qLE3fdZS8NqCUiPp5J48LY0K1EPfhTmzngsVmSkGSZZTExjOs8UkETQJ3m0ANoKy1G29z8oQFh/LcBvCmN+2M/9aam/c+dO5cXXniBlJQU5syZw44dO3jzzTd57733nMd88sknLFq0iMOHDwMwadIk+vTpw3XXXceTTz5Jfn4+9957L3PmzCEsLMx5XlpaGtXV1eTn51NSUsK+ffsAGDRokOe9r7uCHd+u5c33Pua9Fx+re0DZ6vX5ZSDf5tmz2fGvFmTUs3PXTnZt+45R544nKiaGAz/upSA/l+49zyApIrDBpQpaU7/mD59PfHB8u13YnwqUWvgsHLGQuzffrfaOpaSmhAVbFrAvZ5/dSRAJ5ki46WQYD5qD7Gl33vDilVcyiNtqXZ031Gru3JNeT3nNrrsgV/Jo7WJbfibK1RHayZqHDcWQkIAlK0uxDtcRmVLCcXRjvkk6IKYE9m/6L32uqjP+YzuPgfQPfZ4fG9YFa2RXUt37eJ97L+x9C3IPw38uqjvBh2Do0OQoZo/uylvfH+GWd/Zgq/dRtOX5Q8kRWl6tXpdbH79R5G7DzsNTha9xjCRhiI/HPMwz+OPzXF/odPbzGnNuE6lv+ANYsrO5+X2Zokv07DpT52EfyKgsSmqRJYlMPaTm/uQ961PhPddUPQB/bDGqNH/EhbZNRX9vCOO/jaCqNN4OI7fdunVj7dq13H333bz44oskJSXx3HPPubTaKyoq4pdffnH+rNfr+fLLL5k3bx5jxowhKCiIq6++mqeeesrl2tOmTePo0aPOnwcPHgzU1fW73vsFkuJjee7h+Vw6XaEHs6QHyTXlWNYZOWGLpgL1ycJikzmjUyyv7trBqjdfoay0hMROnZn/4KNcM+siwoMCfH5G7tG5qEBtUc344HiR1t8E1Nr7jLhvEXPOWMKrPz+DZKx7OSeYExgcP5iv0r/i66Nfe1yvwFpcm3aXx4TycuWbhnVSFW9SM4jbYl2dN3zV3ElAeGvU3CkJcoUmQWxvHyf6nyhXa7aTPZVIej3x9y2yC2hJkssC3kY9w95tX/2fPRwE7sd6If3PH11+HpI8jnibRJZkU1+kyzJroxNZ9NFkT8dM4vlMqC7zPEeDYOigzhEALoY/tN35Q1mN20hplXdDpFUVuZWch5LGsj8/cx6eSryNY8c4ir9vkYfYn6ZzHT+rXDfqxtl2tf+Gnutjny4iQlHwzyu1ulZ3bg3lnv5BRP6WRWQpFIRAwZmJTOg2if8c+o/Py+SUZUH6VuUsEqX3XK1zcUq/GY3WA/A3Y1lp/kgIM9ElynuWtr8q+ntDkuVWcF21Q4qLiwkPD6eoqMgl0gxQWVlJeno63bp1IzCwaV/29p6S6TdUlSi3VXInqod95FtrQG+kVA7kz1yFhZgb3WNCCDbpKatt52fQ6Qg26RUj/u7fH6XonElnospWpXo/R2nIukvXter3xds48RfUnlGtNZBjQXDy7ge5+c9gBvTIZ+74WOf4BDjng3PsrQAVkLAL76w7nmFX3nVnxK0w7UmPzVabzNnLvlGtRXO8kLYtGN/mU3h3/JHHVa//4PO41TePPHU1d2qCXB6o5CP4URcHq83KZDfDsj5K80dbHsug7MjLDorgvyNm8dil/RWdfMevnssb29K5I+0zwksLXPZFXDaL3Odf8PlMD19j5NUF2wgLqHue9z66kqUlB5WNf7V0Imoz/2SbvWZXMXuo1sl01wGPdPD2Nn+oOUIdnBYRxIlC+2eklB3UKo4OJaPKHAM1lVBTqn6el3/XxuDvY7mh49jRGk+tzZ+Wc0G95V7YpEmNPtfXvhN33mXf2AjTTB8ZibWg3rwUH0/J7ZdzQ8XLPs/9d14Zw4vrdaJxZA6ByntO/T3mmFu86QEk+tnc4mv+cLzF1bIL/cFR2pBxLCL/bYyO0E/dL1BR9HdHttVQpgvDggmDrKNGowqsxWZDkgzOdn5aUYvO1Tf820JpSFtDS1uh6JUvojtnPp3N/ZnWfYhz9+7M3aqGP9hfJJkGA6lRSQzPr9dhPCDE3lZyz7+h5yQwBLp45XelF3oVoWlrdXXe8LuaOy2CXOZomL4cvl7kd6Jc7k5kq83qu11UvXaV7YGwSZMIPf98ZwlPbkAIN24qxhwY4LHPUd6za89fbP8zhNDx41neG5d9AIX/+9BrGnJhmJ6fT7Ox4+QOJnedDNj/LdZSCpJEgAzV9dbCCcZw7vnrdx6KjaVUIRhs7wYAy6IjGVdeodzHW0Uw1JeIVVuaP7SocVtlmRevHsK/vnSL7LVWiYOa87A81/63OQbKHcZYx1T014LaWFWK+Df0XG/7mnKu1+d9doWHc0AXHu6R7q9EfcMf7CUBQYtfYNIVkaqaAI7gw5D6hj/UZg5dZxeWVOlFotaNSIsewMKpvfzG8Ncyf0QGB/DIRf38Z/5oIsL4Fwhk2W5k1UbvCQgBnbKwoDvHimoostZ56A0aJ7OGqvmDNkX/iIAITAZTuy8NOdVoaStkys+lX87v9Moop+iLDOdLXaseQ870J0AXXmfgdz4L1syFgx/C6stweYWGJaHvtQDwLVzkj3V13lCquUvXkE0DpzCNUIsgV3me3QFw10HPtN5WXLQrZQ7Vj0J7Q+t3ua0g6fXONmA1pVXYvtlIaZUFm01GV2+fg+Lans4hZhPBIz0V8lVTiWv5/YZzkXVb2HZim9P4/0/af9hXepRgm40P/8og46pV5Ojs3UGGbHuFVNuvioa/A1mS7M7DQBPDK1WyvxRqyLXOC21h/tCixp1RVElkcADbFoxvfXFULc5DQwBcttIvnYf+hqQwVpvjXF/Xbey53vYpORVkm5XjN97k4zdRoDYwMXuTjY03yaCTPNePssyCvAJlxyHYhSXVb2B3LqZv9RCeVNMD0En2MqNtv+X6jTielvkjv6zaf+aPZkAY/4KOTUUhFP0FtnqRfp3R5+JcBmpkA8U219p+i3vxpAJGva7Bav4AaXlpPhX9C6sLeWPsG+gknSgNaUa0tga6f/cqwraX41iqGRISSJh3maZzo82x7JZ05MhmYoMCGaLToe81zW78u7+wizMYvusuJuvu5Gub90WPv9XVeUOp5s5RHuONU15zp1WQqzTLPpf4SZtGtcyh4upiTedrbWvZFgkx1S2HyqothAZ6OoBLKu3vibAg5aVT2KRJipE7gJh5f6PHxcNgwxa+PfYtXyZ+SY2thudSnwNgvjWM06x/cVpZMQy8EixV8Nt6cgza5u4svZ7dgSZy9HpirVaGVFbVLegVasO1zgu+jvOHTiMNcWS4dz1oFbQ4D4tP+qXzUNDyuDsHZKu18QKFsowhp5Dno+/g4aqPPNaQl5aU+hYc9sWHs+2tax140QOw2mxc/+9d/G/vX5zVPZqLB3cS80crIIx/QcelohAK0j2322pqnQHKCUuOLRlyVIPamzhojJo/QH6lNw9sHXkVeUzrPq3B1xeoo7U1UGiNq2ifJSvLZ9odQJAhiPu33e8p5pV1EuV8DXvK3UMB/2Fj5TCseIYG25oIjVrNncPwH9ApjAMn7EZqqyv6B2s0gv1IkEtL5pAajpp/h4ZFe8Rk0GHUS9RYZUoqlY3/Yofxr7DPgXvkrvjrryndsIHSLVspmt4DgKLqIhZuXeg8p1dUL2aaesNfaZC+xW78p2+BqmJizXXppJJNpvdx2SnodaizhFz7nX8iOpKCeqnO8RYLC/MKmGCIUhSWHNEtymef7vgwE0OTI9nxR57i4ry1Oo24OxwizNoy9fzGEdpGnYeC1sGrQKFGBuq68PWlXzvLvfbl7OO9w+/xvTmImrwCfI0gK5Cq5lysb/iDi9iovs8MD2P5zvPP4JmNv7Lo4wM89tUhckurnftaY/6ICWl/av6+EMa/oGMiy/aIvzd0egg/DYpOuGQGyDojxy2RFOHZzq8+Bp0OSz0NAKNeR1JEoCY1f1mWKbeUY7FZsNZYkWWZoirfNV/QvqNzrYXW1kAepqePtDuHlleFpYIKi6v3Pbs8i5QQHcvLlVsBSsgkkMdw3WF+sPVRfI4WNYibES01dzml1a1Ts6soyhVrV+SW1TQ+/E/NPzU71WfmkBIdRTNEkiRCTAYKymsorVJuDedI+w/1odVSP3IXPOosfv/+eyoPHODDN/4BZ3qOx8P5h9nUa5Td0Ze+xT4xHPocgCGnTyO+Yj9df8zkhg1WYurJh+SGwsqJOnadIVHgVkqWrdfbO4kE9WKCwr+blrpcq03mnCe+Iau4rpzAsTgHWqXTiJLDweijiq7VHaHtwHkoaF3Usop0kZHY3Gr9lTDExrpoho3vMp4Nf35JBsV8HhLMJaXqpXUbzUE8Hh1JlqFu3nM6FxWzBtT1AAD+Pr4HXx08yeHMUhfDH1pn/ogIMqjOgeAH80cLIIx/QcekutQ11V8JmwV0Bojv66IJUGwNoCjfd5pUYnggRr3Op5q/O8VVxWSUZWCx2ReathobueW5vPHbG17P6wjRudaiSZ53L2l3siUMk6mKaoVODQ5lWXUxLzuLzo7g4q2uj9TWRGj8tmZXVZTLWxlI6wtyKXWFySrTZviHB4RTVF3naOxImiEhgXbjv6RS2fivS/vXFmkGMERHE3n9deS/8ipXfGdlV0+9M1rvQEJi2bG1jNMZ0Rcdh7w/4PCXAOh7X8iSH5KI+vhNj2tHlcA9H9t4+hIdu850azsrSUiyzLLSnxl36Av0Z07V3Kc7NsRESWWNx8Ic7IvzuatSiTAbvcmA8dDnaUzsk9CsY1MtO6imng9OTY271RyhSs5DQ5CPk/zPeShofZT0AIIGD+KPSZO9BiYMCQlOUVIHgYZAbuw/hyf3Ps1rEeFcWFqmEP2X2BgRQ0pEoMeYczoXVTuNqIuNAuSXKa+/W2P+KKxQnu/BD+YPUG4H2sS1hTD+BR0TjWr+WGuQgTI5yKnob9BpM/yMel2D1fyLq4o5XnLcY7utNsLYLawb6cXpQtG/FVD1vGtU4nVPu3ty7UmO5ZehS1Z36mgR8+rWrQfyFtdygy/+72yiNaay+QN+WXOnRZQrMAICzH4lyKUk6BcTGINBp20uenrs0x1WMyTUZAQq1CP/tU4Bb2n/Shy7YDDySjgtD849KPPdANdFpL2bQhapp/Vj+LEf4dO/21XfTeHInUcRf/PDOArR6qMDbMDsDTZ295Q8nArO+ePz2xj+RRCU1XNaeanLHZocyejHN1GpYPw7RkNhufo7tCU6BWjJDoowGwk06Mks9hM1bjXnoUuWl4q7Qqj5CxRQEgv0FZgIv/BCxe4Hl/W6gjd/eoUTlLE2JJiLXKL/Elbg8bh45BpPTRinc9FHcEKpxMU+16i3phbzRz2UnIeONoxNWGMI41/QMXBX9NdrW7yVWSSOZZZQY60LLWhR9G+MqJ8sy2SUZXg9psJSwdPnPc0Tu58Qiv6tQFOUeN3T7j4w7+J48QZN981Ra1sU1onDAf2AXXSKCMKolziSV86BE0WMPTNO6691ynGvuasvtuaNU1pzp0WUq7IQLnvbQ+m4tRbtaoJ+uZW5Ps91ZA4Nix/WYYx9dxzO2lKVyH9xhaPmv2FLpxxdGdtG6bjuWxuXb7GRHwJhFZ51+zlFR+0nHN9h/9tWQ/mal7FkZnqWFNWiA2JKoPdxmbRk5aNyJJur4Q9e63J3/JGnGPVvKM3ZKUBLdlBheQ2rbx6CTie1vhq3FudhUBQYA/3KeShoe6gGJoKDsZWVUbRmDdG33Iw+PNzlvCBDEDcMvJVn9j7D61FRXFBaVmfEhyWROvpWsn7xzDhyoKnTiDnG3g2g3vuxNTqNtLn5A9Sdh/Xm7sbOE8L4F7R/lBT9Jd+LW5tk5M9iCRnXul4tiv6NEfVz1Ph7I7M8k8jASJcIckeLzrU2Skq8uvh4LFlZCrJ7gCRhiI/3SLtLCAtE/itU0z1jrSq15V1G8UeePYrUIy6ESLORI3nl7DteqNn4P9Vq3Uo1d3oft2uVmjutolzludB/Vss+iwa0CPqFBYRRUm0vGheZQ56E1jqhSquUo9qOcoCGpP2DXYdl3VCJi3dAbAk88EHdeHbW7Z+pI7aijLKsACyVegyBVsyx5Vi+WgZE+rxHZKn6vlirUrcM9brc5lp0N6ezTusz5ZZV+UcLMS3Ow4p8mPWp3zgPBW0XpcBEYP9+HLl0FtXp6WQ99jhJjz/mcd6VZ17JWwff4mhVIS+eeys99GZiw7owpP915BzbCL/4vrdqcEJntLcrLqkX1ApLotfgfwIRPq/blPnDfV1TP5rvDb+ZP7w6D71rKmhBGP8Cr4wdO5ZBgwaxYsWK1n6UxqGm6C97bx0mAyflaK8pQnqdhE6SXLICGiLq544vw99BTnmOSwRZ0LpIej2GO+7Bev98bKDoAIi/b5FH2l18eCDW8m4ESlFUyQWqRltCQDhDAixQWW8hGRRpV9hNW0OZdRoQSI+4EDpHBrFm30n2HS/U9OynWq1brebOWm9Dq9XstnFRLi2CfsXVxdw+6HY+/PVDkTmkgCPyr1bzr0XtX4khcUMY91c4IQodWxx1+5uG24g4GMGxirp5whBkJThB26K1IMRzm4RdmGuIWlROpS63/qJbh40RusPEUUg2Eeyy9cKm7OZ0IbGJzjr3xXtVjZq4pit+o8jdxpyHgraPUklA4tJHOXr1NRStWUPIpInog0OczgHzsKGYjWZGJ41mbfpaXj++znle7G+rSQpO0nRf1eCErcbV8AcozuCM727nypB/8EHpIMVVT1Od/UrrmnCNc7bfzB8+nYfeNRV8IYz/ejzzzDO88cYbyLLMhAkTePbZZxvVkq0lka1WF8+eedhQxVqets53331HSkoKP//8M0lJScyfP5+5c+d6PefYsWPcfvvtfPPNNwQFBXH1VVfx1D9uIqDet/zAod/4+z+XsWvfz0RFhHHbtbN4IOVvSLJ9sZeRlcM9/1rBngO/8vsff3L1Tbcxf4mntxTsi5PkGDMgNVjUD1wV/Q06AzoNCyoQav7+SNHws3lqxA3cfvBTosoL63ZIEp2WP21Py3MjISwQ0NFZvorfeclDx8HBXSMXoe86xdUw7TIKProZ0tYw/bcHeYYljNIdokdNKWfpsjlwrB+yLHv9LqoZ4i2ltuvXNXdKdXUBCtaUC60ryuUu6qdV0K9LaBeROaRCiDPy72n811htlFfbnca+1P7d0ckwe6PyAtlRt3/+bhmL2zvAUqGjKN17VxkZyAuFw52V3x8L8grU63EdlGS4pOaOSB5FYnggA0u28KDxHZKkOqfFSTmKh2uu54fAMRTV1v0rjekZA+3jVa1NoDeUFu++aHVFbnfnoV5jAMBPnIeC9ol58GCibriB/JUrOfH3/4N6HagMCQlkzZnOWstahTai2eRUeBO2rS0VCwjzDE6EJtnLbKs8tQJARkJisfEd/scAbOg85g+Zxjv71dY1RZXedb5aff5wpyHtQBuBMP5rycnJ4YUXXuDnn3/GaDRy7rnn8sMPPzBq1Khmub4sy5TXlFMlVWHQGTAbzA12LBSvX+9R02NISCD+vkWKxkVbJT09nWnTpjFnzhxWrVrF999/z7x584iNjeXSSy9VPMdqtTJ9+nRiY2PZtm0beXl53HDD9chlOTz/yAIAiktKmXjVPMaNHsbuL//Dr38eZfbdSwiOPo177v4/sNZQVWIk9rQepEydxYpnV/h8VotN1txjuD7uiv5aSTAnCDV/P6SgrJrtSf0pGzaad0cGYsnKIvPhh7GVlqKPUhasSQi3C/JVF/dl+YzlHiJtOkmHTbax/eR2pnef7undveAZOL6TxJK/2GW6neBd9uje+wFw0hZFzq4niBt5maJSrBWdqiHeUmq7fltzp1ZXV10/j9q/RLmURP3CAsI0nRtrjhWZQyp4q/mvv62hxn/5nr0YcgtV99vNdqXveO02nQ1sOkVBL0mSkO66idiAdR6ZH0vPvIEJ6f/y/YDrFtkj0LXow5JYnTyVrgr1vgnk85JxBT+N7E5Wp0keRnqQUUdFjY3Xt6bzwZ6/XIQBtWQVqS3eXX5n2oCiv09nvlD0F5waAvv1tf+Hza2ENSuLqH+9yTUjJcakyYptRH/uG0q5xS4orFgqNnoJ+s7jXNcYsg3e8VaLLhNUkcl7k6zcudPssS4I0Os4PdaX890TLQEG+7P72fwBnus0jQK9jXUeCuO/HhaLhcpK+5ewpqaGuLjmEczafmI7unId1lIrutqGtAadgcTgRMJM2hZsxevX29U83V78lqws+/ZnV7SYA8BmszF//nzeeOMNAgICmDt3LkuWLGmRewG88sordOnSxVlq0Lt3b/bs2cNTTz2lavyvX7+etLQ0jh8/TlKSPVXp6aUPM/u223l0we2EhYaw+uOvqKyqYuUzD2EyBdCvVw9+/fMYy597nlvv/AdWTMQk92LFs89SVmXlzX//2+ezGnQ6Nm/ezLhx41i3bh0LFy7k8OHDjBo1ivfff5+9e/eSkpLCiRMnmD59Om+++SYWvYXjJcdZ/9l6Xn7qZY6lHyMwKJDe/Xvz3DvPYQ42q96vo9fk+iv5ZXZxrIiQQGfaXdn331P06aeUbt7skYoHEB9mTy/LLKpiQvIExnUe5xKNBbhl/S189sdnjEgYQVJIkmuk1hxF9cBrCdj2JMGSa1pvAvlIX82Bov1w8EMPQanfB/+TjKII1d+nJdR2/bJmtw2KcqmJ+hVXK0VZ6hCtQH0T6iXy70j5Dw7QY9Bry9JyYMnxHkHziU1HzHUzKNywy8X5L5lMJD35BL0nTeJr292kZqeSXZ7Ns6nPklGWQXnEafbvanEGXr/j5W6CkMUn6V78JrKk0GFAssfuBv+8DCZeq9gp4Lo3d7IzPd+jI4CvrCJfi3cJCPc3RW4156GLVpB/OQ8FHQfZaiX7qadVdtrfIjN2eo44ZxtRShh+xf95lIqFm8JZPGpxXalY/eDEgQ81PduIWItL696YEBMvffs73/+Rx7zVqXw8bzQHTxRrDgRoCTAARAYHONds4KeK/qoSr/X2N8F52CTj32az8Z///IcbbrihKZfRxJYtW3jyySfZu3cvGRkZfPLJJ1x88cUux7z00ks8+eSTZGRk0LdvX1asWME552irhYiNjeXee++lS5cuGAwG5s6dy+mnn97k5954dCNP7HqCBT0WuGy3WGs4nv0bnUJOI8zkXfRLtlrJeuRR5R6esgwSZD26lOBRozSVAEhBQQ3KOnj77bdJSUlh586d7Nixg9mzZzNmzBgmTpyoePzq1au57bbbvF7z1Vdf5ZprrlHct2PHDia5OTImT57Mm2++SU1NDUajZ6R9x44d9OvXj6ToUCjPB72RyZMmUVVVzd79hxg3Zjg79u7nvLOGYjLVpeNNHjuKRY89z9Yf0zitSzJgr9sPMvr+HN0V/ZcsWcILL7yA2Wzm8ssv5/LLL8dkMvHuu+9SWlrKzJkzee6555h560xyMnOYf9t8UhancP608ykrLSP1h1SQQS/ZSwfqZwXoJT0LRyxkfPJ4n88lOPUUlNtfJFHBdd+tkHFjncZ//IL5Huc4jP+8sipqrDaMes9o7NyBc3lp30s88P0DLsZevDmehcPnc+6Pq+xTgNtwti/QZdj+nOfD1tbcTdbdydc2T6dEfZoi/OVes6ulSwb4oaK/H4lyaRH1A0Qr0EbiSPsvUTL+a3tBhzaw3h/snT6aSsCAs+mxcCnle/ZSeSiN7MeXIVdVEXjmmQAu2Rx5FXk8uedJPvztYy6fsqzWOHU3QH2jNmKlevWm+m7nuDgIrTaZo3nliuf5yirytXiX8TNFbp/OQ8muz+JHzkNBx6J8z14Xh6E7am7M+m1ES248zVkq9tbBt9h6YisDYweqa8RojUaHxHu07j0jPpRpz23lt+xSRjy6iYqaOn0uX5lDWtcrD0zvTUJ4UOvPH+DFeejuLGxe52GTjH+dTsdbb711Soz/srIyBg4cyI033qgY/f3ggw+46667eOmllxgzZgyvvvoqU6dOJS0tjS5dugAwdOhQqqo8hW/Wr19PUFAQX3zxBUeOHCEoKIipU6eyZcsWzj333EY/s2OhpljLXVmFbuK1ZADem7tpQLZnAPw63PtC3sGZqXuRzOrRZXcGDBjA4sWLAejZsycvvPACmzZtUjX+Z8yYwciRI71eMz5efXLIzMz02B8fH4/FYiE3N5fERM+Bn/nXMeIjgiHvd+e2SCQCAoxk5uTZj8nJo2vnunNlIDLant2Rl5PlNP5rrDYXET813BX9H3nkEcaMGQPAzTffzKJFi/jjjz/o3r07ALNmzWLTt5u48JYLycnKwWKxMGH6BJI62zMVzuhzBgBW2UpyaLLTAWCttqI36+neqbvPZxK0Dvll9ghXpLnO+A8eMwYMBqrT06k+coSArl1dzokyB2DUS9RYZbJLqugUEeRx3dPD7Q5Id2MvuzyblO/uYblcyASVd5b6q8y+BF9s/A8bqoYBqAp6NdYQV6rZ1ZAEKxT9faBF1A8gwhRBQVWB82ch6KeNkFrDXknwr8Qh9hfU8GWTedhQDAkJWLKylJ34GjDExTsFvYJHjqBs+3bKtmyl4N33iF+00OXYGafPYEXqCg7lH+Ln0afT9/J3PCNL5hjPiH9DUenh7U1Z21tWkV9mB3lDiyiXHzkPBR2PpmQdOdqIBv+ej76n3bkYHRjN1hNb2XZiG9nl2cSZFTKkk0f7yDhSj1rHhpq4dmQyz2z81cXwB9+ZQ1rXKwnhQc2W0dgkWtF52OS0/5EjR/LCCy/w97//vamX8srUqVOZOnWq6v7ly5dz8803c8sttwCwYsUKvv76a15++WUee8wu2LZ3717V8//3v//Ro0cPoqLsC8/p06fzww8/qBr/VVVVLo6E4mLPlEvHQi0xoJVSSZqJAQMGuPycmJhIdna26vGhoaGEhmprYaaGe2aCXLtgUsxYqCiE6mIkydNz5i565oiAOY7MsoWrX1eyp4Ea9TpNiv71P6f4+HjMZrPT8Hds27HT3r/5zH5ncta5ZzHz3JmMGTeG0eNGM/HCiYRH2J/HKlsJD7D/d6Vc6XfCk+0JLWPZFwVljsh/XVRQHxqKefgwynf8QMnmzUTPnu1yjk4nERcayInCCjKLKj2Mf6vNyhO7n1C8n4yMBCyLjmRceYVvQS83JGSSpDxu16/hKsM3ioJeP4We2yhDXK1mV0MSbMvW3CloHxAUoe1cPxHlyinXtpCbP3w+8cHxHU7Qr6lj2Sn4pyAO1Vilf7CrcMfft8heoqdQt+8LQ0KCR6vQqGuvpWzLVgo//pjYO+9AV8+hHxEYwcTkiaxNX8uHv35I31GL7S2h6n//SzLg4zkN/l1cUBgXTenhrXXx7jeK3G3MedhWaI53ssBOc2QddbPUtRrtHtGdIXFDSM1O5dPfP2XOAIU5RKcHXxlHKlFrq03m/d3HFJ/DV+bQiG5RJIYHqmYP+Z2oXys6D5ts/B84cID33nuPp556itGjR9O/f3/69+/PBRdc0NRLa6a6upq9e/eycKGr93vSpEls375d0zU6d+7M9u3bqaysxGg0snnzZm699VbV4x977DEeeughr9f0ulALNGHbsAqApJBOhHup/S/fs4fjt3pPowfo/NqrmIcN83mcFOQZYfSGe5q9JEnYbOqR8aam/SckJJDplqaUnZ2NwWAgOtrNWyfLUPQXCbEx7Ew96LKroLCYmhoL8bExoDOSEBvtzAKQdUaOWyI5kvcHAFExCt5LGXSSRK+EUMqqrD4V/et/TpIkYTQaKaspc6r5g12YEECv1/P6h6/z464f2b55O6vfWM1zS5/j3XXvclryac7jBS2PlrHsi7xa4z8y2NUhFDp2LOU7fqB083cexj/YX0QnCivIKq706OSRdprsNcorA5kGA6mBJoartvLyTorhQ4/XskPQ68dB3b0a4u5p/Y4Xql8q+ivV1IXEg97k48TWE+VyV/MfEjeEmKAYTefGB8d3SEG/po7lsEAvNf/OtP/Gzc1hkybBsysURXvDpk8j/99v2TfUdwzUvmeUWoUGn302xi5dqDl2jKLPvyDyistd9s86YxZr09ey9s+1/GPYPzAbza51uelbG/V7OAmKso8LN6daXPCZmk5XMuBHdIsiwmz00Apw0KqLdyXnYe36wSd+4jxsKzTHO1lgpzmyjgLiXL+/l/S8hNTsVD767SNu7n8zOkkhr6/PDFDKOALoNU01aq2l9Ectc0ivk7h/em/+/u6PHue1uqif0vzRis7DJlsYa9euBeyeuYMHD3Lw4EE2bNhwSo3/3NxcrFarYqq4uxGpxllnncW0adMYPHgwOp2O888/nxkz1FMqFi1aREpKivPn4uJiOnfu7HKM15ZskgRB9pdfQEgoOqN6Gn7wmDHeB68kYYiPJ3jMGL9o+9fUtP9Ro0bx+eefu2xbv349w4YN86z3ry4FWw2jhg7g0efeJCMrh8R4++e+/rsdmEwBDO1/JkQkM+q887nvwYeoDu1CuT6EovwKdmz5htj4RDp17qL4LLbazIGQBi74KmoqsMk2jhQdcW7Lrch1qeOXJIkhI4cwZOQQ/nbv35g0eBKb1m7ilttvwWzQXpYhaBpaxrIvHDX/0W7Gf8jYsWQ99jjle/ZgLSlB75YRk1Bb91/9zSZ+/783XYyCwJhwRpxrY9eZ3hPms5voAXZ/D+oksMnQ88dHsU68hl1Hizxq45TS+hPDA7lyeGf/U/RXq6lzvHgNgWCpxJ9EuZTU/OPMcXQJUZ6nHHR0Ub+mjmVvav/OyH9QwyP/DsImTSL0/PMV2/UGDRzo6RiIj1ft5iPpdERefRXZjy+jYPVqIi6/zMUpPSx+GMlhyRwtPspX6V9x6Rlu5ZI+U3Odd1LeX1EAa/8Bv37lsrg/KyyJK0OuVe3hDfa5QsmAr7JYvegM2GmVxbtaK1CXjiBK+JfzsK1k/zTHO1lgR0vWkSOirrTdqJB1NKnrJJbtWsaJ0hPsytzFWYlnKd+8zwzXjKOCo/DNw/Dnd3ZtLrPnHNCUzCGwr12gbh3joNVFQd3nj7Ak6OQ7WAu0iPOwyca/xWJh69atBAYG0rdvX0aPbr22JUqp4g1Jl3700Ud59NFHNR1rMpkwmbxHjYbEDSHeHA9eurk52v55Q9LpiP/H3Zy4d4HC+lQ9MtBaNDXtf+7cubzwwgukpKQwZ84cduzYwZtvvsl7773nPOaTTz5h0aJFHE61Z3ZMOu8s+pzRnevueIAnH7iL/IIi7v3XCuZcPZOw0BBkWw0zLr+eJY8s49pb/s698+fzferPvPnCcm69c77L9+TwzwcAKC8rIz8vl3379hEQEECfPn00PX9xVTH5lfke2x112ya9id27dvPDlh8YPW400THR7N+7n/y8fLr37E5CcIJfpvm7R6Ydi1Zf+/wdLWPZF460//o1/wAByckEdO9O9Z9/UrZtG2FupUvxYYGMPnmAM9a87TFN6HOLuOdjePoSvDoAYqzW2s65dROD7Pg/BbXu+qh9zXQShFVncfMjz7Op8gzn9sTwQGYMTOS1LekeC/vMokqe2fibl7vVccpqdrWo+QdGwNRl8PUivxDlUlPzzy7PJru8rtxKiPp50tSx7FXwr9Yh0Ji0//o46vbd8eYYUCPikkvIefY5qn79lfLduwkeUXddSZK4tOelLN+7nI9++8jT+Peamls7MYz+P4VuIZ0gugekfwd7PFsBSsUZPMaTFOruZINtGMMV9EQevEDZgH/+m98pKK8hyhxAgEEis7guo6nVFu++WoEmDoKMn2o3+q/zMN4cz8IRC9uE7kdzvJMFdTQq6wj7N1jJtggyBDGt+zQ++OUDPvr1I3XjH+zffUfGkSzDzx9D1kHY9RqMXehxeFNLf1Z+nw7A38f3YFT3mNYX9VObP4pPQvFnPk5uOedhk43/WbNmER0dzZo1awgLC8Nms9G/f3+++OKL5ng+TcTExKDX6xVTxb1FmFsavc6u0P7EduW6XbA7KCw2C0a9yoKiohCK/iJscGdYfBdZL76DJafOsPQWGWirdOvWjbVr13L33Xfz4osvkpSUxHPPPcell1wCVSVgraEoN4tffvnFab3o9Xq+fOdZ5i16jDEX3URQoImrZ07hqQfuBuBYUQ1FVhMvrfqIpf/8B+eMGUVYeATXzbmd62+93eX+V0yp03lIO7CP/37wPsnJyRw5csTns8uyTEaZdwlHm2zj9ITTeemHl1j12ipKS0pJOi2JhQ8v5OqZV2tu/3gqKV6/XvHFEX/fIgDVfe3pe+mNfAW1fwchY8eS/+eflG7e7GH8J4QaGLt/jeI1Hcvx2Rts7O4pISu8uGw14awqv5QRkR+4LNCrzImsLBrKbcYvUF7Ya0v/C67OBeqM/4yiSl7dkq54bEMSCk9Zza4WNf/STDBHw10HPdPyTvGiXYuaf6Qpkn+e9U+e2P2Ex+JeiPo1jZB6af/uwYPiCnvkv7Fp/1pQcwyooQ8LI3zGDAo/+ICC1e+6GP9gF/577sfnOJB7gF/yf+HMKLeUfLXU3HqOL+v4B0g98B9yio8RG9aFIf2vQy/pYFmySuTb7op8NmQlhdX/IZ48556TchQP1VxPSdUAj7N+zy7lja1/ArBs1gDG94rzKCs65Yt3Lc7Dshy4bGWbcB6mbE5h+djlYo7ogDQ06wjsJcJqpcSX9ryUD375gE3HNlFQWUBkYKTica4XlOCcFPjwJvjhZRh1O7h1O3PU7WcWVapJBaqW/vx0vJDUY4UY9RLXndWV2NBWdiBpmT8MgWBxODlPnfOwyW+x9PR01qxZw969e9m3bx/PPvssBQUFvk9sRgICAhg6dCgbNmxg5syZzu0bNmzgoosuOqXP4s6E5AnoLDp0Ba6RO0dNt8Vm4VjJMbqGdaXSWumsDzcbzEiVRVBQt9AOO3cEoWOGUX7gMJa8Qgxde2MefV6LRlg3b97ssW3NmjUtdj8H5513HqmpqXUbKgoh62ew2Rdgs6ePZHbGfiisEwbp0imRL95xbW0mA9WygWKbfRLo2bsvb3201uu9fzpu//4mR5s9RP2UGDt2rFOQ0FHjf/FVF3PxVRe7HHf7/Nu5ff7t1Nhq6NunL1s2bqHcUu76b97KEX+lCH7Jpk32lDE3r7AlK4sTd9ypeB1LVpb9nGdXtHsHgMVqo6jWMHCv+QcIHTeW/H//m9LvtiBbrS7jteuJ34itLFK9toRdbbfPcfg52XN/VdaFpMeNRrr9ARfDtSpuOI//axM/yj14Keq/6EtdF6U1g67DuOVxn79bNhE+j2kIp7xmV2tNXWmWa4SildCi5l9QZV9oOVovtcW0Xn8l1GR3wssylFdbCTbVLZEcHQCakvbfEkRefTWFH3xAycaN1GRmYkxIcO6LDopmfOfxrD+6ng9//ZD7z7rf8wLuqbn1HF+KEeTf32Nh1xlM8JryLmOqLsRdSSdRyudl4wru+ULP2DPmE1db9iTLMos/O0iNVWZ8rzgm9I5DkqTWV+TW4jwsPtEmnIdyrVNm2a5ljOs8TswVHRCtWUf66Ciylj1B9eHD5Kx4lsSHPfUXekf3pk90H9Ly0vj8j8+5vu/1ivf0KD/pdSH66B72zlx73oIxd7gcr9dJLL6wD39blaoYppBRL/1Zuf0IABcOSGp9wx+0zR+WShh7H6SuPKXOwyYb/0G14nEBAQFUV1dz5513Mm7cuCY/mDulpaX8/ntdG7f09HT27dtHVFQUXbp0ISUlheuuu45hw4YxatQoXnvtNY4dO8bcuXOb/VkayuhOo/mz6k8SQhLQB+idhl6NrYY/i/6k0lLJLwW/OA1IsDsHEi01uMeAJb2O4EG16ec6I+h8NdBqB1QUujhBnDjq5yUDyJ5pmo5PM0OOUvW76XUSOknSpOavhCzLLgZ8jVVZqMgdi82CJEkEG4M1HX8qUIru6+PjkauqlLUmvInH1Dafz1r6GKHnn99mSgAaQ1FFjfOjiFAwDIIGD0YXFoa1sJCKn37CPKSuHju6qkTTPZJrwvgZ12PHR9/Fp4cS6HF6iIfhGg6cHhvM1zkj+G7abYwP+sNlUfpNWib95ddIkPIVW/DZZMgkml22XpqeTwm/UPQP1qh07CeCXFrV/HPKc1z6uguah0CjDr1OwmqTKa2yuBj/TVH7b0kCzzwD8/DhlO/eTfby5YSce55LVG/WGbNYf3Q9X/72OefnJVCVlUFoYhcGTLgSg7H2Hafg+PIaQU57neXmICaUV3h9NvdRLgGyBP+QV/LPjydx4zk9yC6p4o/sUr7/PY8Ag44lF/ZtPSe4+/xRorERcxtxHsrIZJZnkpqdKuYOgQvujgHdA//k6DXXUvi//xFx+eUE9evrcc6lPS8lLS+Nj377iOv6XOcxblXLT/pPY8Lm52DHCzDiVnsru3pM6ZfIy9cO8dAVAhjZLUqx9Ce7uJIv9tuN59ljujb4928RtAYfok8/5c7DJhv/f//738nPz2fmzJncfvvtjB49WlN6dEPZs2ePi1PBIQZyww03sHLlSq644gry8vJ4+OGHycjIoF+/fqxdu5bkZIVwWSsgSRJmo5lAU92XPEAfQFRgFDnlOS6GP9iNw+M6ic46HWFqyvq2Gnvananx9fV+T62av1ckCSK6QtEJZ2YA1Cn6F6FuYFttMskxZkDyqebvTnFVMRllGS4iflq96f6m5l+8fr1idN+apXHyUkKWsWRmUr5nb4NSWdsaDrG/8CAjBr2nKS0ZDISccw7FX35J6bebXYz/yM6JaNHp/+f0p5nV1UB2eTbP7H2GrPIssmvV8nvEhSieM6hzJH/klLHvrxLGT3JdlK49mM3HNdfzSsAK3M10x389VHMdNkXXgG/unnAG7+8+5vLibhVFf1O4j5NaT5ALPKMiUYHaMiK8iskKGo0kSYSYDBRV1FBSaSG+nvf9VKT9N5bAfv0o372b4s8+p/gzu1iuo/Rq5MQJjP/TzKy1RYSXPOU8Z1fYMmx33sjZ19zrcT3fEeTGtxnVAUlSHsW/buWqw3ku+yb1iadLdCuJ3SrNH0EaM5TaoPNQIPCGeehQwi64gOIvviDrkUdIfu9dj3XxtG7TeGrPU/xZ9CfvH36fcFO4Mwvt2+PfqjsPj65hecxpTMj9C1Lfhrg+HkbvlH6JTOyT4Cz9Kam08M81B9l1JJ+DJ4ro18n13b565zFqrDJDkyMZcFpES388yjQl+HCKnYeNfovdfffdDBw4kAEDBhAcHMyiRYtYuXIlaWlpfPrpp835jIBrarUa8+bNY968ec1+75ZClmUKKr2XSGTq9YTabOqiXRojzW2WWjV/r9hqQGeA+L724601oDdSbA2gKN97ZALAYpOJMDcsmlNcVczxkuMe2602q89zjTqjX6n5y1YrWUsfa3QbGF9Yctr3QiOvVL3e30HIuHF243/zt8TdU6dinHjOKH40hRBRVao6xg0JCYQMH8Hw2uyJP4v+5LX9r/Fn+Q6gq7rx3yWCj1L/IvV4PrszdzsNzD6RA9mYlkWZbQTp41+h+56HXRa8EvCE5XK+tjXcYeNI6//7+B78fXyPU1ezqyaqU1W/pMJ/1PxBOSoSERDh9ZyOruZ/KnAY/+7t/or9NO2/eP168leu9NjuKL0quXQ8t33o2Sc9vNiG9K832QYeDgDfEWRHm9FAhldqU+d2J45Cj21f7s/gggEZ/iPqV+Ep3OuKcB4K2i9x/7iXkm++oWLfPorWrMGY1MmlJDQkIIT+Mf3ZlbmLpbuW1p0XFEeVrcp7+UlkGONyQb9uEcj11s1hSXYh0j4z0OtcS392H8nn030nefTLQ7x78zCkYzugNIvqoFje+8E+D80e3bXFPg+vKLYTTrBnaKvaMK03fzTa+B87diz79+/nyy+/5Oeff0av19O3b18GDBjAsWPHGDDAU9ClQyPLWMvKsVRWIhmM6ILNznRxb9RIEuWSRLCaYaY32o22ekYvASHqMt5tDa3ODWsNMlAmB2HBhEHWYdBpM2YNDSyd0CLq543WVPNXqukv37PXQ+ilOTHEtu+FRoEXsT8HIWePAb2eqt9+p/qvvwg47TQAAirLkfCuyB+/YIFL2cSk5Em8tv81yvQ/g65S1fgf3DkCQ+hBfuJzbvq6zggON8ZQZZpCJ/Nwup0zDc6+vM5b/dN78PtGJgUc5JWKi2pjfMpoSes/JTW7WkR1gqLsqYV+IMgF6inVhdWFqucINf9TgyOyX1Lp+u4pcab9+0/k36vjtnZb8EebAM85RgfYAN1zK7FcfkddCQANiCDr9TREQLQ+anoiD32exsQ+CadO3E/L/AG0BedhdGA0ekmPVVYOQgjnoaAhGOPjiZk7l5zly8m4/59QLwvZkJBA1pzp7LLs8jgvuyLbY1t9ZGQyLaWkBpoYXumW+1icYXfEXf6Ox7v53kln8tXBTMKOfEXVUzcQWGFftwYAa+Qongu5hSn9XEWVTwmq7YS9ratbd/5o9FvsoosuchHTq6io4ODBg+zfv59NmzZxwQUXNMsDtgdKt22jRq+n2mJBV2toSkYjthhtqu4Wld6cANSU23tn1vcs6YwQfhoERTTxyVsBd0eGWhcEN8osEscyS1xq9/UaDGyj3p7m3xC0OG3AXgJQPxPAqDOSEJzQYDV/XxkvWlFT7A+d3EKCfJKEIT7eo0dseyO/rFbsz6xu/OsjIjAPHkz5nj3kr3yboEGD0EdHkffmv4moKqUgIISwkED0+bl1J9WO+6r0P12udUbkGZwW3IW/yo5hCj1McvRMlPireieBnVZ59PAtqsklsNMq+ofaRbWQ6qWbdRkFzw9hsCWN83WpbLINVTTwbz23G5/9lHFq0/rV0CKqU5EPsz61v2RbUZALtCn6hweEE2gIFGr+rYCj3V9ppVvk35n27z+Rfy2OW28+cB0QWWRl/8b3GTK1TrBLa2Q49pz5sP1V1/EXmmQXsaooQMmg9qYnImPvKLIrPf/Uif1pmT/ALupXXm9+9kPnYV5lnsoZwnkoaBzG02pb8rqVH1uysoj615uMuETntRWxN3IUtaBqVyzrFtqFSOt9VztHmXmsdzozf12B5JbUm0A+j1meQPqlv31Muqfgt9T7Xovz0BQGphC/CT5AM9T8OwgKCmL48OEMHy5EROpTvH492QsXIj/6KJWyjKPiX66pwZCRR3AElAV6N1IN3ow/pZeWraZWIK9b23IA1LY1dHFkSL4nFZtk5M9iCRnXycmqwWhOighscBRei+EPkGBOwKg3NlnNv7raHlnWN0E0T62m35KZScHb7zTuovWdUu4OqtrfU6lHbHujLvLv3SgwdOoEe/ZQsGoVBatWObdbdAbuH3Mrf5s9kelkO7MyajIzyViwgNyXXibkvPMI6msX3JEkiX4R5/BX2WpCotMwKugMWG1WntrzhH25p/KVO1SzCqvNvuB3UeMdcRv67c/yTMynTK08i7+K68ZjfQN//pTerd+KC7SL6pTnQv9ZLfssGtCi6F9UXcTTY59GJ+mEmv8pxhn5r5f2b7PJzp/Dgvwn8t9cJVUlGcdcfh4SN4R4c7zq99QZQR7xfzDi/zwX2Ye/rI2ENU5PJLukcaUEjULr/DHlMQhNbBPOw9CAUMwGs3AeCpqEbLWS/cSTKjtln62IfRFrtWIFUgNN5Oj1xFqtDKmsQo9s76JxdLtrHbzNyszM5wGFTCbJ3mSUdQtBtqm03lzW/Ma2FudhVTFc/h+/CD44aPJbbPbs2fTr14++ffvSr18/Onfu3BzP1S5wpORJ5RVIm78jd+pUiIwgUJKcX9zQIokSvfokbkCPrgZcOl5KBgiJhZJMvHqbco9BjKltlABUFkOxkrCf9xp6GcgiDJutWvUYnU5CVyvo58Cg0xEXFoBJslHpo2ZRlmUqLBVYZSt6SY8sy9hqVEQY62GrsaGv/R9WqLJqkXZzu4bNRk5ODmazGYOhccO1yTX9koQuPBydyYSlngCgIT6e+PsWAXhmFNTua+9t/gDyy+zfPaU2fw6K16+nWEULRW+zkFiWR2ZpDcHn19XZy7JM6TffUPL115yYP5+ERYuwFhZhiI0lWh4KrKbGlEZZTZlH1wingaky9CUJ8quyef3A63z464eui8SgWBZGxDCh8He2XHCSQ1WxVBScICiyE71Gnoe+9nvoXo93ynD36LdTUa68ijymdZ/Wwk8jcCekNrJfP/JfVm1xTp/+pPbfXCVVoYldXH7W6/QsHLGQuzffrXi8jOwaQXYXquozw56261YDKwFrbSN86onEhQZ63d8kGivKFZrY6mr+oM15WFJdwjNjnxHOQ0GT8JVZpMPeirj3cZm05IbZGQE2mWN6PYs6J5FVb20bb7GwMK/A3kmkJAPSt9aNVdmGruSk+rrG4TT43w2eO72UEzSJNhZ8cNBk4//WW29l//79fP755yxevJhff/2V3r17s2PHjuZ4vjZN/YFj+OwzLED22POQjEYXg7ywGGoMYLTYU/Rskv1ngKjAKI5Ul0F1GRjN9tQRvQEKM6HUXlcjA9WShA0JHTIBcr1K3UIrGFrwRdocyLJ9kHuLqEt6+2dW/xidgZqAcLIqctXPqyU2xG6YWWUZvSQhGfTkloGvMystlRRVFbnU0OkkHTbZu/Gvl/Tozdq6BvhCp9PRpUuXRl+rQTX9KhH8xIcfcukDW7+VFOB1X3unoNb4j1JJ+3c6X7xw24FPWV/oWqsmSRIJSxZTtn07NX/8yfFb5jj3TQiL4texwezuW8Z3x7/zMBK1Gpgv7nvRY1t2RS4pkWaWVwcx4cu76Vv/u76zhbznWlES1dH5asnpZ6JcJiHK5c840/7rRf4dYn8Beh2BRv+Z18zDhmJISLA7ZVWcu7ba4LtiS0+gKFzPiAlXeuzrHd0bCUkxwtwtrBvndznf+8P1mWFP23UY2nl/wOalnKc/SHhNKUV4apU4BENHdNPo0Gsoqor+3nQLWnf+cEc4DwWnCq2ZRZGlDb92tU5iSaxn8CBbryclLobl2blMWLfIpdRGDorwqo/kPA4l/4B6OUGDaOPthB002fgfPXo0o0fXTYpbtmxh06ZNTb1su6D+wJFkGeOnnyJ//TVyRISL8R84cQTGHXsIK61bZBcEQ9r03oy58Wn48GbI/AkmLYWetWUVv34N39/P9sBAXo8II09f908ZbbUwp7CY0ZWVMOlR6Da5xX/XJvHXHth6p+/jZrwEOhOU59nr75IGs+mXXJZ+e8jnqfdN6835vRs2+Laf2M7j+x5v0DkOFo5YSPdO3Rt1rjsBAQFOrQgtuIv6WTS264u84QZKvv7aawRfrWWfe4/YjkR+uffIvy/niwTEVRRiPPgTXDrQ9dzdu7GVlHicYy7O597P4GmDjvVd1nss8ppiOLq08jp+0rWVV0t5z7WgJqrjkvXj/6JcJp3J6zlClKt1caT9uxj/tfX+/pTyD/Z5N/6+RfaSLhXHbdml4wn5cJNd3M/9fMB2x2wXsT8Hq9JWISNzVsJZ3DrwVnLKczDoDCzcspD04nT2ZO3x3Su+fvsqmw3S1hCSncaNhnU8a5nlXTC0uWt2NSn6+9f8AULRX9B6aM0sKjTL9DlqI7IUCkLgUGcJdDrCA8IxGUwu778EcwLX9b6G5XuewqoQ0JIlCUmWldcfFYWankfdQaBSTqAVJedhYITvp/Ej56GDJr/JioqKCA+v67d47rnn8tprrzX1su0CpYEjVVYiuRkCoe94pgNHAmc/m0FBl3UkZu62vwBjOkNgbRQ/NIqNtlxSQmKQLZVgrfu6Z8oyd4XA8vJcJoRG1Z3jr1RkQqln2zx3bJVZ7AweT7atkjgpkBGBZsKCzZwo8d1eLyoshMAGfA5Wm5WlqUvJqlY3nMMCwggyBHlMbAtGLGB88njN92pOlET9dPXGpzdCx48nfv4/OmwEv7Hk+4j8a/We1+S6HuctY0DCHrWbvcFGSq+tlNeUYzbWtY/0VbPri7pWXu5qvPW852dMgeM7T00NWztS9K+y1X2e7pFVIcrV+jgi/yX10v4d/+1PKf8OwiZNgmdXeC292tb7KXTPvkVksWfG2uDTPRfBJdUlfPzbxwDM7jfbxcjflbmLD375gFd+esW38V8fnQ7Omw//m83tQRv4QprJ78V133EXwVClRXZTanY1zR+RYAzym/kDlJ2HgXrv6xjhPBQ0F1oyi6oM8PcvZKJL6/bnhsLbE+HK2xYzrvM4V02huCGkZqcqGv4OZElSXH84zpBl5Wpmm2yv/feJ1lT9+qg5DysL6/3gf85DNZps/J977rmUlZVxxhln0K9fPwIDA9m/f39zPFubR8vAUcPRhifj0UdImJBl172L7Orcb+08ksdjYuxfM7dR4PScxcQwrvNI/Osrh6dHv57R4o2/f36StSU/OH+OCzUR4kOpv7FphFrq6oqri1k+drnf1NWpifrZioqUT3BQT5W/I0fwG4uvmn+t3vOjcpDLz1rr7bofqeS7v75jare6sgG9Ts/5Xc7n3cPverwo1V6cSqiq8RafgOW9FdSvW6gkoB0q+kcERHhERYQoV+ujmPbvVPr3r8i/g7BJk7yWXp19zb1YLr+D/RvfpyTjGF+X7iZp26+cvx9Ozp9P148/ovqPP53nfhz0M+WWck4PP53RSa4Rq5v73cxHv33ErsxdpGalMiRe3ch0j1oPOfMC9LG9MOYcZv3Yw+zsfLOnYKjaIrspWUea5o8CmLXSL+YPUHceVlrrNIqE81DQknjNLKrFZIEAt7T/6BJI+djKaWNt6JP1Hk5CraUrWXo9uz3EAGsrgN0MfVtDTKyGpuC3weCDL5r8Jvvpp5+wWq388ssvHDx4kPz8fD777LPmeLY2j8+UPB8OAR0QlF9GVl4gCZ0D7Z7pWlJzfyJL78Nzprcf1yDvfEuj5NH3oegvI5EhR7GuxDWNPrukiuwSMOolaqyypr7jWmlrdXWaRf06sCp/S+Go+Y9WMf59OwElsoPC2R7cmWqLjQCDfTw0pN5u/ZH1LsZ/XkUea3773P6DzQT6Ou+5bAmnunA4ptiNPq8da/WSVVPuppjRXCUBSum+bUxUR4vzsLC6kDfGvuE3zkOBnRBH2n9lXZeL4kpH2r//Rf4d+HLcGowBznZ+8fmHuTZoFr1OWOmUnc0f509ArqqbI3qG6RkxQWb6jdd7aM0khiRy0ekX8dFvH/Hq/ld5deKrivdTilrHm+NZ2P8CJnxzGN2OFxiVOBD0JaCLB0bbIx6qi+wmZB21sflDOA8F/oJaZpE+Ph5bSQlyeblHmr29y5BE1tLHCD3/fI+1pdaSlCeiIymod259McAiQoikzuuQSTT/qrmGJQGriSPfLv7nQSNT8NtY8EELTTb+Z8yYQf/+/RkwYAADBgzgzDPPbFB9cnvHW0pe6ORJmtqsbZbMXBnpqsar1TjVetwpQc2j7yKe594ayP6zt9ZAEeYAHrqwL//6Mq1Rfcc9ohNxQ7T3OfaTujqton76iAisBQXOnzuSKn9LUFljpazabiCrRf611OW+OfBibJKO7JJKTou0Z8JozRgoCIG9x7eQv30L+vwSDLGxLCv/L+XWEqyViZSnz0NvPoZkKEG2hGIt74YEBEbtAX2R4gJTkmXiaz3t2mkGQR0l52BoEkSfru18PxHVaWvOw/q4a4Z0tNKfUIXIvz+n/TeGXlG9OLfnJDYO/Jrrv7FBles4Dy+2cs/HkHBuIPT0PP+W/rew5vc1bD+5nf05+xkQO8Blv1rUOrs8m5T0/7E8KokJ+SfhvcvrdoYlwZDZPhbZjcw60jov+Mn8IZyHAn9CKbNItlk5fuNN6ifJMpbMTMr37PVwSjrKErPLs9UdXLJMgZstWV8M8M3CO5DREUch2USw29YLGzpuHdWD+B13oiziKcPEfzV8bdLGnIdaaLLxP2rUKLZt20ZVVRUrV65k69atjBw5kmuvvZYbb7yxOZ6xzaOWkle+Z68m4//L2CBiwiKo/nOtc4Kvrz7vDX8xTn2nzUi1NXeuaTPV5gTuKLzCa2ugnJIqIoMD2LZgfIP7jqtFJ/pF9/N6nr/V1WmNEsctWoQxPr7DLuybm8Jye0RQr5MI85IS7Ksu988fDVBQQVZxnfGvtWzowgOBJH9eTlbJbXXbQiF3gp7NpksBI9ZyV+NZBsozLiDotFWKit4ysCCvsBElQ00Q1FFzDpactP/xSuuJ6ig5Dw06ba9Wv5mfa1HSDDEkJHQoB6Ej8l+/5t/f0/4bw9x+t5L1j68U9+mwj8K8x58kcuJkj3fEaaGncUH3C/j0j0955adXuLHfjc7v/8CYgapRa6eYaDCMy8dTTHTzUm0P39Cso+ieoDN46SjkX6Jcbdl5KGifuGcWFX3xpabzlNamjlaiKZtTlDuKqNQmOkqaH4+JodwykJPFdXZQYm2wb3C/ROgc6RlEcDgD0jdD34vVxUSVMg8NriWZqviJ81ALTX6TffDBB+zbt8/58zfffMOXX35JWloaDzzwAP/617+aeot2gVJKns/FvSRREAo/ddFxd/WfsHUBAJGmSCosFT7vmWBO8Bvj1HfajKyYNrOuMJmvPzjg8/LZJZUN7juuFp3IKs9ycQb4Y12de3ROU/8TwBgfL2r6mxFnvb85wGcrRm91uQl/bOevggoyi+qJ23jJGLBh/yeXgKEHyj2W2VElcO8nVipHFLA96TTF57GU9OOq5H/yTc7rHlGmsRG9mXBkA95bYHmhoYI6WmrqAkLsLU/B7bjWE9VRch5GBUZRY63xcpb/OQ9BXTPEkpVl3/7sig7hAFAS/GsLaf8NpdMfxVg9G4k4kUA1cgcwZ8AcPvvjM7ae2MrWE1ud2yNNkRRUFXgc78C7mGhj8VISEHMGrJpZz/D3L1EuJeehXtL2HP7mPBR0HLRmJqodNyF5AsvHLvd4f/5/e/cdHlWV9wH8e2cmvRcyAaQqohCKhLKABQTBoCKKqK8romJB11WMDVxfEdcVC7Kwuriyq4L6rrK6oiJIiAVBUBISEJAiaChCeu9l5r5/TGYy5d6ZOy3Tvp/nySMzd+YWk3PuPb9zzu84rD8EAaVq4J+3J0NsPle6s896mdFYLdDeDPz7RqDwHUNHg3miPuPIIcA2aBCdCji4n/tb8FAJtxv/0dHROHbsGAYNMowNu/zyy/HUU09h586dyMzMZOPfDkfJNERRxJtTVRCteq+NBaNHZA+Ut5TLrsX7+JjH7TdOPb2Ujr39KmwM6BvLDRn9dQORpo9EapyyB4K0OOdWNFAypy4hIgFP/+5pvJT/kl/Nq5PqnXPILKkfeU515zJ/yTHKGgVy83K1CYa/35K6Fov35UYMVEQlImbhI4h69XkIDc02sR9jwtAFBz/EDz2HQi+TV2Nyn6l44tIbTA+fZxvPYlXhKnxbexR7s/6Mi3autr0RWve6SYnVOle/KJlT19YATHoSKFzrF0l15IKHVS2GpcMSwxNR01bjl8FDa3ZzhnT2wsjN3ww2cZ1D+6WH/QdPz7/S0WJynztWfUzy/mnvwd2cdDJRd8hMCTD2+MemA5c8Auz8q1/UH4B08DApIgltujY73/LP4CGFFiUjEzXp6XafOaf2m2qzGkBpYykWf7fY4fGrWiow41w7HVnmy4waDbsBOPChVYZ+dI4cmiu9H2NdEpnY+T3/Ch66yu072T/+8Q/cdNNNuPjiizF8+HD8/PPP6OjogCAIaG93FC0huYd7ITwc/7o+Fnn962S/q1Kp8Mplr9g0To3ONp6Vjiqr1J5fSsdIbr8pEhMHJVhn9E9wsK6yN7P517bWIikyCTmzc6T/H/qAXO+cBSb16zaVZj3/7kiPNzT+S60a/4DliIGm4lLM//xXHEwZiO39ElDfID8CSAWgR1MThlb8ggM9LMufeblRqwSLpKAnak/g018+xVNntmD9/T/g8OGPUF53Cj3i+2LU0Fugfm2U4WYpFzhTaYCSg8CGe5TXL0pHCqScCyw86J2gpROUBA8jNBF4Zbxt/ezr4CFgO3JI1OvsBxPtzN8MNsah/Q2tHRBFEYIgmHr+44Jkzj/gXs+d8e/fHXaTiQJwedSRdXDS2ON/8cPAuHuAMfN9Xn8A8sFDY/AkMSIRNa2BETyk0KNkJQDtYsfPnGqV5WoA+SX5io7v9KgXvQ44uVNmo4J6JjwauGYVkLPYb4KH7nC78T98+HDk5eXho48+wsGDB9GzZ09s2rQJTU1NmD17tifOMeiZP9y3HD2CsueXQd/Whj0ptXbX5CptKrVsnJ7+Hj2+eg4/xyThhfhwrNizAm8eeNMiEq+N1mJRzymY+uWL8OhSOoCdJXrOOuzVk8voX9vc1fvii2z+5U3lNpWTrzjM6C8IUCUkQBURYYjGdmJSP+8xZvpPlkn2p5Sx8V9Sa9v4B7pGDBSdqcX+H1RIjA5D2W97oWQmWg/xF5hn7XJUbh4f+zi+L/4ep+pPYcp/p6Gpo8m0TXv8fSwae1tn/SHzcK7vAHIW2b5vXr9YD8mLUXgjj9VKR/S7mZLgoU397AfBQ0B65JAqPl7Rd5X2Fgcy47B/nV5ES7seUeFq1HXeh+IdBKMDScSokaiOVyGhTjqVrgigJkGNQaNG2mxT8vcvR1EyUakRPkpHHcnZ9Tdg7N1+UX8oCh6qIyQ7d/wheEgEyHdeGunqHCwzDdtA9EWjRtpNBujyqBclowvtqTsLRKf4ReeDJ7h9Jzty5Ag2btyIxMREzJgxAxkZGYjvfJB45pln3N19yDA+3MeMG4v6rVvRvKcAl/wk4tPx9hu1Fo3T1BFAzl8wurIEuf2uREH1IZsheGVNZcg+/n9YER2JyU3NKLRZQ9PFbN1K5uyGRRvm3QAWn1OW0T8MkRq1xbBopdn8Adt5dcmRykYK+NOcOocZ/UUR+poa9H77bQgqFZP6dYMqDzX+5Yb9W/ul3LC0zXk9YlETKyhq/LelWFbzjspNfHg8Zp03C2v2r7Fo+AOd9ccv72PF1CcwNe8dqwh4b+Cyx4HNjwGSw1Y75+VufMh2dFCUo/LoX3PqAjF4CMiPHNLXyY8wM6e0tziQRYerTR1Z9a3tiApXo9445z+Iev73Vv6IN6cCj3xsmCIkded9e7KIsErb5YLdXUVIPploZzm/9FHDj/lDdp9xwN9G2B91ZI+riUi9IJCDh0TmpHIZNe/fj/JXXkHpshcQnZmJjvIKyedRuQSzz9x9Fe7HO7JTml0a9eJsHiK5ffhB8NAT3G78Z2Vl4a677kJNTQ3eeOMNHDhwAI2NjTh69Kgnzi8kJVx7LZr3FODSg3p8+jvBbu+/ReNUEw70Hg39ye9wuv6U5OeN2XaXpibjBVFEqabrT8C0hqYrN0klUbX2JsmIvpKM/jVN7fi/+aOgUglOZfMHpOfVpUSkQCWooLdYZrCLr+fUSS231VFepui7uspKJFx9lZfPkADzOf/eG/Zv7peyzsZ/WizixoxDRdzrSK6XfnAXAdTEAA/8YQ4e2tuI+rMliOuVjouuvgyaMPmqX6fX4dPjn0puM9QfAl4s/hqXPlCIH3/6d9eUgGFzoT69W6bhb3ZWzVWA9WyF5iqzF/43py4YgocORw7ZE0I5QwRBQGyEBvUtHWho6UBaHFDXOec/mIb9lzeVI2+wCq9cD9yeq0eqWfI/YzBgYIko2dBX+ndtnbxLI2jw0rlzMPXES1BUzq2fQa58sXN0YTclIvWSQA0eEkmxzmUUPWY0GnfsQFNeHn69dhZgNgXcuHoMANkEsynPvYXVT92JZ8K3WDy3R6gj8MIlL7g26sUTmfgDKJu/I243/tPT0/GnP/3J4j2dw7lcZE/8lVei9M/PoU9FGwaWiPi1p20DV7Zx2m8CCkvzUdbRILt/URBQo1bbFDrzNTSnOnuTdGPOrtKM/hWNrbh2ZG+nTktuXl1la6Xsd3w9p04yGqpNgyohUdH3Q6F3zl9UeXjOf0lti2mesZTj5V2N/1E9h+Lxq5Ix/4Mqm567zj52xLQCUb9/DLrKKsR2bitaZbl0m3Wg6dA5ot1eKREiSppKMPXj6ZZTio6/j0Xay+DWYNSoJCAsyq/m1EkFD6PU9sdc+Dp4KMXhyCE5IZgzJM7Y+O9M+mdc6i+Yhv0bG/B5g1XIHyTgwtMikhqA6lggvklE9iciZv0govlgMRrL8ywC0ebrdEOvt/ju4T4CoFJBG63Fpus24ceKH3Gq7hSe3/082vRtiB04GbgxQybnkINyPmSmYdqQVEZupYlIfSAYgodESgkqFeJnZKEpL8+i4Q90rh7z4ENQJSbaTTCr/ecmbMnNwd7KH7GvbB/+tvdv0Ov1GNvTxZwz/SYY6hiXRg7518hDT3D7TjZ9+nS8++67mDu3K1OiOkQeELxFHReHuKlTULf5C1x6UERRT+v4uJ3Gab/xKC94TdmBrBoYxjU0X0xJwuSYHs6t8a30phqrhQ4q5OmHmDL6p8RI975b80ZG//jweERpovxmTp38cltlQKmDnv8Q6p3zF57q+U+LjwAAtHboUdvcjkSrYIJOLyKvqAqFJw2N7QGpMVCr1Mi6YylWtC3EvFydRc9dVSwgiEByI6CrrLLYl/nSbQBsAk2RqQkYe6keeYOlp+AYSU4pKvoPVkRHYWqT46VIJTVXAzestVju05dz6uSCh826ruvzx4RckiOHypQFaFUJCdDXds3VDMWcIbGRGqAWaGgxJP3ryvYfPD3/5g14UQUc6mf5PJB7Uo8r9uoRtWgFTum77tHGnrtFYxfhgzds656KOGDdFcDN9z6BcE04xqSPwZj0MThafRTvH3kf7x56F+OnrrbN+6G0nEst4+VwSoDvHt6lgoeRavvPMv4YPCRSStTpUPGPN2Q2GsqnvqbGzg4MCWZbC/dhzLixGK0djc1Fm3G85ji2ntiKG86/wfmTUqntjBwyf+3/Iw89MfXH7cZ/Xl4e3nrrLSxduhRjx47FsGHDMGzYMFx99dXu7jqoGB/elQ5Zj585E3Wbv8D0gzrkTItDsWiWdMte4/Scseihd329XFEQutbgtfdB62W8YnoYCoZebtSH4ea7pWEAlr74NYrNEpuFq+0P3fdmRv+6tjqsmLQCKkHl8zl1SoblqmJjoW/sXOucGf19rqrRENVOcrPxHxmmRlJ0GKqb2lFS12LR+N9ysBhLNx6yKDOLPj6AP1+rx5UZU4F7V+LZEcuQfLTE1PtWMygdr7zWCDRKJNzpjKwXP73E0Miz+ntTV9TikY+BV66HwwCAxW6NUwJSUzH51G9Qu7pud1OFYUkeH1MSPEwMT0SEJsJvgoeA9MghdWoqhHBlf6O9V64M+ZwhxqR/9a0daO3Qo01naPzGBdFSf2qVGovGLkL2tmzJANZPfYCpewFBbxmcNwYPh915B3p9bHu/T6kHsj/W4ZxJeqBf1/u3XngrPjjyAXac2YFfa3/FwISBdqcW2n3glZp3a/fBHj55eJcLHrbouupyfwweErnD5VFmVtpLS9G42zDq6Jbm4fiz/hg2/rLRtcY/ID9yyDjqCHBtRJIXSQUPtdFaLBq7yK1nDLfvZJs3bwYA1NXV4eDBgzh48CC+/PJLNv7NSD2893SQdCt24kSoowWgSYUPhdn4edpkZY3TiFiMSroA2o5SlGk0rj5+o7ylyrllAu3OwTPczPYOfQL3/d+PNp9q04kWn+zujP6VzZWYMXCGU/v2BiUVpr6hAal//CNqPvzQalpA6PXO+QNTtn83h/0DgDY+0tD4r23BBemGpKlbDhbjvvcKbcpMRX0r7nuvEK/fOgpXZtiulXvBiQ78Vnmn/ME6k0NKMZbB23P1yB8kQHSi3IkQUaIWDMHDlla4NC/XT+bVKQke1rTV4F+T/uUXwUNAfuSQrkLBkOjOkUMxY8eEXGPfWmxnD39DS4dpyL9KAGLCg6fxDxjW2V4xaYXNw2V6ZBoe2NUIATW2X+r826p6ey2kagYBAAQBpc8vQ9yUKaa/pb7xfXFZn8uw7fQ2vHfoPTw9/mnZ83LpgdfRg303P7wHavCQyF2eWhWmbNky6KoNIwwzAPw9Dlh7xR6cueQMesc6NwXYRGrkkPmoI1dHJHmBXPCwrKkM2duysWLSCpfrCZfvZKtWrcJDDz2Eo0ePYtCgQYiPj8eECRMwYULwzInwBLmH95LaFrOHd9sAgBAWhoT+bag6FIb6XUcxZu7jio+p7jcRi358E9naHrLZMh05WXcS0/873fbmK7dMoPH16PnAz1/Y3Hx105fh/s9iIUI+oVmoZ/RXWmGG9+uH87760mZYb6g/sHc3URS75vzHuD8cOD0hEkdK6k1J/3R6EUs3HpIsvcY5/Us3HsIVQ9JtkkLV7tnk1rkIAFLrgaEnRehVlvN5lQQDyic+AOT/27IeiOsFdLQYhvb72dBcKYEWPFQ0cig+Hvr6zjHaHDkkK66z57+htcMi2Z/KyQB0IJjaTyZ4WGEneAgAejvT9TqH7TbtKbBIBHbbkNuw7fQ2bPxlIx686EEkRibafNWtB15HD/bdKBCDh0Se4Km8U8aGv1FKPfDIx3p8338lbrjnZdd3bC9jv59k87cXPDSNssx7EZP7THapvnC58Z+RkQEAePjhh3Hs2DHExcVh6NChyMjIQEZGBq66itnGnXt4t3qoaK5GQp9qVB1KQ8POPdDV1UEtsxazzfzOc36Hqd+/hhXN4XghJcmyAR+lRYuuGXWttRDtrCKw+sfVNu+ZLxMoPadXAH7eAjz4I3B6t8XNN6+oBsW1P8geD/B8Rv/YsFg73/D9vDrr35s6RVmwQtOjh012Vep+jW0603Bgd+f8A+ZJ/wzrX+cVVVmMFrImAiiubUFeURXGn5tisc1TN99HPhUR09xVg1XFq/DWVNHhdIAeg64EJj5p+xB+ZJPfDc01sg4eRmmULKToP8FDRSOH6uo4ckgB4/D++pZ21LUEX7I/a54OHhpZB7RHa0fjguQLcKTqCD78+UPcPfxui+0eeeD1k4f3QAseEnlK9OhMaNLT0VFaKh2MFgTL3DIKV6ARYFiJpNebW6C/cxlUmuCtkx0FD42JlwvLCl1aDcTl/3NTpkwBID3sf+vWrX7d+L/uuuuwbds2TJkyBR999JHibc5y5+EdVUWISOxARJKI1uo21G3ZgqQbb7TZh2Rm+LQe0A6KxFQcx+Rbf0ZhwymLqPI3Xy9G9m+bIYiAaNauFkTDH5Tc0oLGZQJfTEnC5KZmiYSAomEt3dO7bW6+ZfX2lzAz8mRG/4Z2+RUPfD2vTur3pkpIsP8lJvTzK8Yh/5FhKkR7YDiw1tj47+z5V1pmpD7n8OarkHnDHwCS60U88rGIFdcL2D1Yup5IikgyBNSkHsL9bGiukVTwUCW5gGIXfwsedpQqS+jHkUOOmc/5Nw77j4sInmR/jngqeGi9H0EQMHfIXPzpuz/hg0P/xo2NQ4HKatPfYGG5dx94vck6eBiuUhYQ9pfgIZGnCGo1tE8uNkxBEwTJUWY9n10KwDbhsCopCXqrHn9zKgBJtR346esPMWza/3jj9P2CM8uBusLtJ9Zbb70Vq1evRnx8PGpqatCjRw+sWrXK3d161YMPPog777wT69atc2qbs9x5eEd1EQQBSBiWiLLttah67/+gio6xeFCTzQxfXoEzZcnAxCrEn87DmAuv6dooipj68w6saKjAC70HoNRsSUBteDxml57C35MTZc/VIiFgS6vkZ/T1Jdj9S6VF773SwZLeyOjvb/Pq5H5v5hm2bXBYrt+p8uB8f6Ar4/+Pv9Xg+18qkRoboex7EmXG4c1XFKFKTJRM+GdX52fn5eqQP0gDvUT7uLG9ET9X/4zzk86XzhniR0NzAfngoR5dw5r9LSmXS8HDThw55FhsZ89/Q0tHV6b/IO75t6YoeKhSGbbJbNekpyPqopGmhF3GZ5es/ln45t1luH5TCc7Wz+/6vFaLxruuVHR+rj7weotU8FBw8NTj6+AhkTfFT5sGrFopsWy15SizuClTbILYZx93PM258NBXdhv/3siQ703W5xupUdYWcjV46PbdbP/+/YiPj8ehQ4fw6KOP4pJLLsG3336LlStXurtrr5k8eTK2bdvm9DZnKW3IpsVF2qwGMK7qBFQAVMlpAGrR9vPPOPvoowAMN9W0RU+g7IUX5dfJBFC6Nx5xRbsgmDf+T+cBZYcwVROFybM+R2H9r12FI3UEcv71OwDttvu0Um6nAfrAxrPYXN81xD85Jhyt7XKrABh4M6O/P82rUzQvNzEBqohIi548Dsv1P1VNxvn+7jf+txwsxvKcowCAQ2fr8D///AHJ0WEO02jaKzOObr4ApIMDDhjzAYwvT8RObY3pfW20FnHhcThecxzzt85HhDoCFc0VFttNCbv8ZGhuyAQPAY4cckKsxZz/zmH/QbTMnyNKeu6S77gdVW+9LVt/hA8ciF+mTbese9LTEX/VDNz9QY3N59tLS5H2l3UYe73K8bQiP+otlwseWgcL/Sl4SNQd4qdNs2ncW48ysw5EN+7OU7TvHY37Mev7XRYjh4z79VaGfG/xxchDtxv/YWFhEEURa9euxZNPPolbb70VmZmuP1xs374dL7/8MgoKClBcXIwNGzZg1qxZFp9ZvXo1Xn75ZRQXF2Po0KFYuXIlLrnE9w+S1sYOSEbPhEiU1LbIPlqqVQJ+OluL7P/ss5gi8LfonZh0OhIlO4/ZfKejtBRnFz7s8PgdTRo07dqGGPPpZAVvG/6bcT3UMSkYE2M53aDH8FuAY45HPfTQ2TbmRQgoFpOxpX6gxfvGHtLU2HBUNLQxo7+jebk1tej9Npfb8nemTP9uNv7lkoJWNckH4ZSWGYc3X4nggPU673KWXfg4jo9JtwioNXU0YfZns1HcWIx61Ft83hMZaj0tGIOHAGQbbBw5pEycWc9/XXNXwr9QoqTnLmrECJvtQnQUxKZmNO3aZbPPjpISVL75luFzVtuM83kdrTKSHp2OEakjkF+S7/PyGIjBQ6Lu5OwoMyWjjprDgXmf1OPsu2Yjh9LToX1yMfIGq7yWId8bfDXy0O3G/7333osxY8agqqoKS5YsAQA0Gtchd0FjYyNGjBiBO+64A7Nnz7bZvn79eixcuBCrV6/GxIkT8cYbbyArKwuHDh1C3759AQCZmZlobbUdkr5161b06tXL5XNzllolYMk1Q3Dfe4WyPXg6vYjnNh22eT+17SxKCxNMiQEtONFL13HmBNBaD0TEGbJs/7TBsCHzDsnPjxr7ILRH16FMEKUTAooi0nU6jGpps3y78wqXts+FXiZipVGrsPqWUfjzJstlD5Vm9JcaxhOsGf11lZVIuNp/82ZQV1AryY1h//aSgholRmkQGaZxeRUMezdfqeCAqNfh9B0OMn0DCE/T2sy7jdZEo0PfIfl5T2So9bRgDB4CgDox0SJTMkcOOSe2c35/fWsH6kMg4Z8cR8FDqe2RI0fg+ISJ0Ms8B9oL76tgGFV04WkRh/upJBvVqVGpmLFhhl/06gVa8JDI39kdddQpss3wY66jtBRnHlqIL25KgjjAOxnyPc2XwUOn7mYnT57E/v37odVqMXas4WHynnvuwY033giNRoOYmBgcP34c48aNc/mEsrKykJWVJbt9xYoVmD9/Pu666y4AwMqVK5GTk4PXX38dy5YtAwAUFBS4fHylWltbLQIMdXV1kp+7MqMnXr91FJZutGzw9kyIxMKpg/C/nxy0WOfeqFdlBZqbwxTPlZejiewwDPU/bwrw4weGpba0GcA5oyU/r9aEY9HA2cgu+giCKB0A+H2vSUDtNuS3VaJcrUYPnQ5DVcl4uOYm5OjlI3wltS1IignHd09cbjHFQUlGf6lhMT2ieiA5wn7j35fz6mxWYRidCXWPVEXf9VTCJXJMaVm2VuWBnn9HSUEBoKa5A/93S6ZLq2AoYR0cEHU6h5l65YaPF5YVorxZvkFtTNi1p3RPtz8MSwUPT9WfUvTdQAsepi1ejDCtNuRGDrlalq2Zz/kPxWH/5hz13EkN25Vr+Ct1Y+o0vB59wGb1nob2BhysPGjzeV/16gVa8DBQeKocU2CSG3Wk1qZBX10DtLXZfkk0NKFnbapC7v1qyZFD/pYw1JfBQ8WN//fffx+333472tvbIQgCLrroInzxxRfo0aMHEhMTTZ8777zzPJIsT0pbWxsKCgqwaNEii/enTZuGXRJDzLxp2bJlWLp0qaLPXpnRE1cMSbdp8OYVVUk2/MPRjsTmBjQjya1z1MSHIyqlDY25G9BxpBma7/6J6HBAyLxdNqM/AExNGYEVu/9hWCbQbCmNMFFEuyDg9Yo8rO2tRWVL17b4sFSUtkfDaqSvjbL6FqhVgu3qBnbIDYspby5HeXM51IIaOlHnV/PqpFdhSIO6p4OeWs7L7XbOlGVz1U3u9/x7cxUMVymJvMsNH1f6MPzItkdQ29Y1tcDbPXdSwcOYsBg0tttvpPhb8FBpUDBMqw3JhH6ulmVrFnP+TcP+Q6/n3xVKA1T2JPUagJyZyy2CdSNSR2Dyh5NR12bbEOyOXj3J4GFdYAUPA4WnyjEFLldGJRrzEV14WsThPob/JjUA1bHA4T5dU4nsPad0Z6JAXwYPFd/Nli5dirlz5+LJJ5/E6dOn8dhjj2HRokV48803PXpC9lRUVECn00Gr1Vq8r9VqUaJgKKTR9OnTUVhYiMbGRpxzzjnYsGEDxowZ43CbucWLFyM7O9v0uq6uDn369JE9plSDV+7Bv7dQgbAo+wnyLMgl7FKF45fPteho+QrAVwAATXQ6tON6IF5uX3odsPVJTG1qxuSmZhRGRph69we1tuGW3uk4HQY0tVRafK2uvQKRvd9Dy5lb0VGfIXuqXsnmH5GIJ8c9iZfyX/KLeXWyqzCUlaGjrMyQJVmv57xcP+FsWTYy9fzHut74dyYpaHeSi7wDQI9HH5EdPq70Ide84Q94t+dOLnhobPgPSR6Cw1WGqVd+HTzUahE2YID9L4Z48NDVsmzNNOffYth/aPb8O8udUWt6AFVxQNyYcVCr1Ba9c/kl+ZINfyNv9uoFYvAwkHmqHFNgsx5VVL1xo6Lvjf5ZxAMb9Ug164ysiAPWXmFIJpoSlSKZM8SbiQL9beSh4sb/r7/+ipycHPTr1w8DBw7Eu+++i1GjRnVr499IsOq1FkXR5j17cnJyXNpmLiIiAhERypbikiP3QN9PKEV0jzYgCtA3Q3oGfedDnnbREyh94UXLoTHJydA1NKCjpgHW3+5oEnDmkcVAWLT0A/zJXab1t9WAxXJ+OgAtxgarzP/vCO1GdNQPsTmuN7P5V7ZUIikyCTmzc3y+tIeShFzqpCSk/+9TNr83zsv1DVfLcnWjoVHgzlJ/jpKCulpuPME68l7z3/+i6fvv0ZyXD8yfL/mdUWmjoI3WoqypzG7Azpq3eu6UBA+rWqqw/LLl/h88LC21WAGEwUNbnrgvA2Y9/y0dqDMu9Reiw/6d5Shhl2j2X+tnGwHAJ1el4KWettMSvb3utRyHwcOUIThc6V/BQ0B65FCg1AueKscUXIo01YhS8Lmr9tjWO8n1wCMf67FqtgZPRj+JsqYy0zZttBYzBszA2p/WeiVRoD8GDxU3/js6OhAV1fW/ffDgwdDr9SgpKUF6errHT0xKamoq1Gq1TS9/WVmZzWiAQCD34N9HKIOgAipGJiLl+xq7D3nx06YhespU7P38G9SfLUFcr3SMzLoURZMuhq6tFdI5dUWULn0acVOm2N4MGuQb2oWRESjXyP/JCAIghNVCE12EjqZzLY4IeDebf3lTuU1PgS8oScilq6yEOikZ5331ZcDenMl8qT/XGwX2koK6U248xTzyHpUxFL9cdTUavv0WTXv3Ivqii2w+r1apsWjsImRvy7aZhuOIN3rulAQPS5pKAi94uORpBg+9yDjnv02nR0WDIQAez2H/ijhcJlAU8dk4FSYesuyZA4B2NXD1VQ9KljulvV+e7CVTFDxs9q/gISAzcqgzGzrrBwpUJeclIy7O0JC3vxCebctHBcPIolu3tuEP55UCZs9UpU2lePuntyX3427HhL+OPHT0/8/CunXrsGvXLjQ0NAAANBoNmpqaPH5ScsLDw5GZmYnc3FyL93NzczFhwoRuOw9PMT74A5Z/qP0Eww3kSO/+KH/0GWisAhsarRa9V61E/LRp2HKwGJcs/xZzdrfhztPJmLO7Dfc+/i/oahpg++dvJKCjshZN+RLracbKB1HKFTZME+MspzOkJ0Ti9VtHKcpMrtPrkF+Sj82/bkZ+SX7QZvPvKC83NawSrr4KMePGsuEfYDy11J8xKWh6guVIIGfKTXcI798fCbOuBQBUvPqq7Oem9puKFZNWIC06zeL9hPAERcfxZM+dK8HDGQNnYEz6GJ/01ikKHlZXm4KHfdetQ6/ly9F33Tqc99WXfLD3kNjwroZ+cY3hfsZh/8rFT5uG3qtWSj67nPO3VRj97Co8+2gvPHOLCqtmqvDM/6hwvG8YwnXAoHe+k9yncVSRIPNcI0BAenS6R3vJnA0evjX9Lbx4yYt4a/pb2DJ7i88a/mceWmhTjxizoddt3drt50TkCT3itFh7hcq0LKg5Pbo6T+RaPuariTjDvGPCGc6MPLR+XtJGa72awFRxKPviiy/Gc889h/r6eqhUKgwYMAAtLS148803MXXqVGRmZiI+XnYmuWINDQ04fvy46XVRURH27duH5ORk9O3bF9nZ2Zg7dy5Gjx6N8ePHY82aNTh16hQWLFjg9rF9QWo1gH6CYTjKKTENwuAxuPSrGyR7iOXWBx9YfUDRsTsO7wJ+N97yzX4TgPheQF0xrBcn7KFTlofg/ktG4cKki5zOTC41NCYxPNFuD6Kv59RZD61TpygLVjCbf2DT60VTwj93hv0bySUF9VWPv5zU++5H7Wcb0bjrezTm5SFmrHRSuan9pmJyn8kWPek6vQ53597t8BjuBPKs59UlRCgLOARy8JA8T6USEBuhQUNrB9p0hsdMDvt3jr1lAqcCNvXD0JticXL2HNTn5qJhxw7EXnKJxf6UjCpyt5fMuv4obbTf8Dfyl5GHdkcOdU7XLH1+mfSoTyI/NyptFE5e1BMrUIJ5uTqLkUNVccDuCwRcle+4YZ/U4Nrxne2Y8OeRh4ob/9u3bwcAHDt2DAUFBSgsLERBQYFpiT2VSoVBgwbh8GHbNeudsWfPHkyePNn02pj0Y968eVi7di1uuukmVFZW4tlnn0VxcTEyMjKwefNm9OvXz63j+pL1g//EbfVADXBK1OL9L45gRJ9EdKSei7KI3oZGgaAC7KwProm0jolJU0d0oHF3nu2w8ytfBP5zG2A1EPmiljZoOzpQqtZIhtZEERA7EpCkPt+pbP6A/NCYmrYa2e/4ek6d1NA6VWKifAJGIOQTcgWL2uZ26Dt/xYkeaPwD0klB/U34Ob2ReMNs1Lz/Acr/9jdEv/uubL4V64dhnV7nMB+AOz13UsHDMMF+g43BQ5JjbPwbMdu/8+wFqGway+lA8q23omrdOpQ89xwGbNiAlgMHLZ5PjKOKrMu5RtDgpUtfcquXTKr+iA9X1qHlL8FDhyOHRBEdJSVo2lPAwCEFHFMAsCkb+YMEXHBab8rmf6SPCheeFnFVvuNOyupY147vqJwHUvDQ6bvZoEGDMGjQINx8882m94qKirBnzx7s3bvX7ROaNGkSRDvzHQHg/vvvx/333+/2sfyJ6cFfFIFNvwEABp6fgW+PiLjpje9NDQ0A6JkQiZvH9JFdH/zH1HMxO2obOppVkB0AI4g4+9oG6KrWmt7qmhM2E7jxHYhbnoDQmfwPADqi05FYOhElvXYDEjn/BAFoqx+C9PgYp65dydCYhPAERGoi/WpOnVRSLn1NjfyXmJAraBjn+8dFaBCucWr2VMBLXbAAtf/9GM17ClD55lsIS09XlLNCSc/d9YOudymQJxc8bBfbTf/2p6VAAQYP/V1spAYwSy7Pxr/3pf7xAdRt3oz2k6dw/NLLoG/o6qIzPp9MnTbNNGrgVN0p/GX3X9Cub1fcAJfKuv3N6W8k6w97qwsA/hc8tEgIaocnlmMk8gXzAOChfl1/7+nR6bjr1seg+XqZ3WSjlXHAkd7AkJN6yWUApSgp51LBw9gwZVEGXwQPPXI3GzBgAAYMGIA5c+Z4YnehraEUaG8CBBVGZGQARw5bNPwBoLi2BX/98pjsLnaLQxA+SoeOnSoY/tzN/6g7dyYK0FVZLrdlnBOGVSuxq9cY/LllFfq0/Yg01KAMidjXfiFadAI04iBEaDdCCOv6vqiLgKBuRUTSboiRPyO/RKN4+IqSoTG1bbV4ZdIrUAkqnybkApQl5VIlJEAVGWlxM2ZCruBhnO+f5OZ8/0AUptUievx4NH77LcqXLze9ryShlFzPXaQ6Ei26Frx3+D1MHzAdlc2Visu5ouVAwxMRoYlg8JAUM2b8B4CYcDU06tAK8vmCOjYWcTNmoHrdOouGP2D5fBI/bRrGpI/BmPQxKCwrxGe/fIb/HvsvRqaNtLt/qQf0tKg0tOpbHSYnDYzgobJpThw5RIFMalqh8Tmh7klIJxuFoSWkF4C/v65Hiln1Yr4MoCtTiuQ6Hxra7c8v8GXwkKFsf1N9AgAgxvfGi7lFLu1CDxWe196Klyb+A2WFCeho7vqDVUfpIXYI0LfLjNsXBJxc+hz+cPFj0AkqnMEQm4911GdAVz8EqugiCJp6iB1x0Df1R0Sv9QhL2I8FX95rUQgcrZOpdB5NZXMlZgycoeiz3qQkKZe+tha9V66EoFIxm38QqvJQsr9AVLd1Kxq//dbmfeuHczlSN+4hyUNwT+492F+xH9d/ej10YtfQPUf1h5LgYU1bDf416V8MHpJi5j39cZzv3y1EnQ71OVtkNkrPWb/h/Bvw2S+fIedEDp4Y8wRiw6V72+Qe0MuayyQ/by0xIhHVrdWm1/4ZPKyV/oIRRw5RkJAbJh8/bRqwaqVNYEydlIj22jqk1eltmvbGZQD3PnQ53k49bPM8kZ2ZLVvOlXQ+AP4XPGTj399UGRr8dZHnoLhUeli/Elv1Y5E0IBzPX/gemn+pQEeLGppIHcSoVJzebOeLoghNZTmGVPyKAz3Ok/xIYnQYIjVqlNR1LefXMyESM0dehX8X7Xe4TmaoJOXSVVYi4eqrvHw25AumZH8h1vg3NVwlNypPKCV14559/mzsr9hv0fAHHK+zy+AheYN5z398FB+VuoOhbNgJ5EnMWR/ZYyQGJgzEr7W/YnPRZtw4+Eabryl9QLfn8TGPQxujDYjgIQC7S0SzHqFgJpVsNOqikTg++XJ0VFZKLgMoAhi7/iBuys3B3sofUd5Ujo9+/gj5pfk4VX9K9lhKOh8A/woeAm42/gsLC5GRkYHw8NB6APaqzp7/6sjeir9ivT640aRZd0I1ZBFiTu4yTCeI1aL2YA2w+XGH+0xurZfdVtPUjv+bPwoqlWDKTJ7ZLwEzNlwp+XnzdTL1ot5mPVyNYP/P0N/m1TEpF1U1GuaSJ3ko2V+gcCahVPToTMlM31J0eh1W71stvUsH6+z6Yv1vdzB4GBgsGv/s+e8Wzqx2YSQIAq4fdD2W71mO/x77r2TjX+kDuj3aGK3Ps/kDyoKHAKBOTISuuquxwZFDFEqsk4027s6DTqLhb/o8gI6SErQW7sOYzu+lRqUif2s+Nv26CY+MfgQxYbb5zJR2PvhL8NDIrcb/mDFjcPjwYZx//vmeOh+qNvT8C8kDFH384ann44P8UxbJ/6LC1PjrTSO61gcf0LVkjqYsT9F+qyLi7G6vaGzFtSO7AhT5Jfl2b67GdTIf+fYRm20dYldGZX8bGiM1rw6RkfJfADi0LgR09fyHVqNA6cN5/ddf4+wTT1iUG3s5ARw9nJuvs2v9AD4qbRQSIxJR01oj+V2/Cx4mM3gYCGIthv2z5787KP2bt/7czHNnYlXhKhyqPITDlYdxYcqFFtudXaLLnK/rD2tK6+C0xYsRptVy5BARXAssjkkfg/7x/XGi7gQ2F23GnPNt89op7VTwl+ChkVt3NEdZ+ckFncP++wwcgp6HIlFS2yLZqy8ASE+IxAOXn4cHLj8PeUVVyD9RhRW5P6NDp8fo/tIPmNGjM6FJT7ebDbM8KhE/pQ60e5ppcZYNYHdurkaBkpQLLWbTMTi0LuTo9CKOFBuyQNe3dECnF6G2kyk2mCh9OK9et87mPXs5AZTWH1KfK28uR5uuTfLzfhk8jIiw/yUGD/1CnMWw/9AK8vmKo+cTubKRFJmEKX2nYMuJLfjvsf/iqZSnLLa7OurH1/UH4PrIwzCtlsv5EXVyJbAoCAJuOP8GLN+zHB8e/RA3DLrBZmnjUWmjoI3WynZe+Fvw0Ijpa/1N57B/VcoALLnGkGzPullhfL3kmiFQqwTTMoEPThmEEX0S0a4X8f5u6TkqgloN7ZOLIYoi9DKn8GWfTOgF6T8NAYb5/WMHWN6APDGktqatBn+5+C94a/pbePGSF/HW9LewZfYWnzT8FSXlSkyEJi3N4j2NVoveDhKeUeDacrAYF7/4NbYfqwAAfJB/Ghe/+DW2HCz28Zl1D+PDuc06n0p0lqXS55dB39aGxt15qP18Exp356FHRIqiXVjXMzq9Dot2LEJTRxPOiT0HadGW5VEbrZXNFeBtxuChzRDd1tauf0utlwoGD/2BeZI/DvvvHsbnE8ML6TpGrmzMPn82AGDTr5vQ1N5ksS0jJQNhKvnfoQABieGJ0EZrLY/lw/oDMNQhx6dMxal583D20Udxat48/PaHB+x/SRCgSU9n8JDIjMNnF5lyc+251yJcFY7DVYfxU+VPNl9Tq9SyuYT8IXgoh2PZ/ElrA9DYmXk2qT+u7JWE128dhaUbD1kM609PiMSSa4Z0Des3c/uEfnh4fQ3e230SCyadizCJ5Yl29RqGd8fOw737P0GPlq7ssM3qcETp2nDNyR/wRf/xqIxOtBh1YB10MGeMfpU1lbmVVCegknLV1KD3228zKVeI2HKwGPe9V2jz111S24L73ivE67eOkiyTwcT4cC65lI699emNOnMCHL9sksV81EStFtMmxyN3QD2g1+PC06LNGryR6kgMTx1ukTB019ldKCgtQLQmGm9c8QZ6x/aWXP6nuykNHqoiIpjR309x2L9vyGXrBoCUe++RLRtj08finNhzcKbuNL7b+A+MCx9sSPSVOQrP7X4O7fp2ye8ZH9CXTFgiu3yYL8iNPBSbzAIbHHlIpIjdZ5dOUuUmMTIRV/S/Apt+3YQPf/4QGakZFttbda3YemIrACAmLAaN7Y1d+/NxUj97eEfzJ529/ohMBKKSAABXZvTEFUPSkVdUZUquN3ZAsuww4xnDeuIvm46gtK4VWw6W4JoRvSy26/SiIZjQaxi+7zkUQyt+RXJrPaoi4vBzUh+89N3rOL/mN/yz6GM8OOYuJJ782bS9cuAQPH1thmQDR61SY9HYRcjeli05b19pQIBJucgfGcuN1F+xCENgbOnGQ7hiSHrQTwGQezjXaLWImz4N1evecbgP84Y/AHSUlWH+ByJ6jFNh4iE9Us3yjXatwduCO3PuRElTCcqaLJfnmnXeLPSN7wsAfjGvjsHDwBfLYf8+Y52tu/7LL1G/ZQvqvvgCqfffD5VEkmmVoMLd1cPR440TSK3/J852vt+aEouSy5qgukCDu4fdjU+Of2J3aqE/1B8MHhJ5nr3AYo/sh2XLzZzz52DTr5vwRdEXeHT0o4gL78qJ9u6hd3Gm4QzSotPwycxPcKT6iF8EDx1h49+fGBv/Vsn+jMP6lYjQqHHLuL7421fHsG7XCZvGf15RlWkUgV5Q2Szn9/yYuXh120rEHTuEf555yiLKrDmuhXbMk4BM7+bUflOxYtIKvPjDMiQfLTH13FUP7olHxz2Ol/Jfkh0Z4Mt5MdZz6qJHZ0KIcpDUrxOTcoUG83IjRQRQXNuCvKIqxWU1kEktpWPM7q+k8W9DFCEAmLnbdjJSSucavH+9XoUfsF/y6+8feR9j0sf4TYSdwcPAZ97zz2H/3c88W3fspEloLihA+8lTqHrrbaQuuNfm83Vbt+KC5Z/ZvB9W2YBHPgZOPHEtZlz0AO4bcZ/f9O7LYfCQyDusn11qN3yMxp270Hr0Z9nvjEobZVpOdNOvm3DzBTcDAEobS7Fm/xoAwMOZDyMuIs4vgodKsPHvTzoz/SOpv1u7+f24vlj9zXHsOVmNg2dqkdE7wbStrF6+AQMApTEp2Nz/d7jp2DeWw8tg6J2TS9hlNPaoHqtX69BR2vUQr9F2QJsEuyMDAN/Mi5FKyKVOSYGol8uI0IlJuUKKo3Lj7OeCgfVSOoCChF2O9in3niDg9i/12D3IMAVAitxSgN4mGTwMV9ZYZPDQf0WHdf0dldQ2h1RiT3+jjo1B2uOP4+xjj6HiH/9AwsxrENarq2ND1Olw8tklUMO2DlEB0APo81YuxNuWQK1W+/0DOoOHRN5j/uwS3r8/GnfuQt2WLUh77FGEabW2nxcE3Dj4RryQ9wLWH12PgQkDUdFcgQ3HN6C5oxkje4zEVQMCqxwy4Z+/0OuAk7sM/xY0htcu0sZHYsYwQ+/82l0nLLZZZ+m3phL1uPy07bxmABYJu0Sd7fmZElyVWma9NAYNxh7VY8WkFX6TlEsuIZeushL66mqoYmMNbzApV8hzVG6c/VywUpKwyyWiiOQ6Qy4Ayc1mSwF2J6mEXMcuvRRnn/pf+19kUi6/tuVgMf7w766/pb99fTykEnv6o/irr0L06NEQW1pQsuwFi4Sh9bt/gKaiRnYNbxUATXkNGvKVLXXcnUSdzuJaRJ0OQoTttAYpDB4SuScqYyiiRmcCHR2o/vf7sp+7euDV0Kg0OF5zHPO3zscTO57AD8U/AAAu73O5zSoA/s6tnv8lS5YgNTXVU+cSug59Bmx5AqjrnKV28EPg1E7gyheBITNd2uW8Cf3x2Y9n8em+M7jiwjS0dOiRFheJtLgIqARAL9Mpl1Hxq0USQBudCbsa8/IthptFXTRSfo6aKAKCgNLnl2HKV1/6RVIdRXPqYqLR87k/o/SFF23mNnNeXWgZOyAZPRMcL71pvQpGKJKbV6dKSoLeaq6/s5Ia7G/3xJKjSskl5NJVVgEAVAkJ0NfWMilXgGFiT/8kCAK0//u/KLruOjTk5qIhN9e0TR8Xo6gn6/gv+bjod+O9d5JOkht5qO/osP9Fjjwk8pjk227DmT0FqFm/HqkL7oUqKsrmM/kl+ejQS5fLvxb+FX3i+/jNtEMl3G78k5sOfQb85zbA+lGjrtjw/o3vuBQAGNU3EX2To3Gqqgn3vtfVg2Gv4S8ASG6tl95o5czChYYHW+N+HT3YdwYNmvYUIGbcWJ8Pu1Myp66jtAzqpGSc99WXtsN6+dAeUtQqAUuuGYL73iuEACheBSNUSeUEiLpoJH6ZNt3lKQGAIYeIPd2VMFRR8DAyEj2XPsPgYQBhYk//1nbyBCAxJU+ob7T9sITqGA+fkBvkg4eVAABVfDz0dXUMHhJ5WdyUKQjr3RvtZ86gduNGJN14o8V2nV6HF/JesLsPX007dBWH/fuSXmfo8Zd91ACwZZFLUwByfirBqaomm/eNDf9bx/VFzwTLIcrpCZGYd7WySLJ5wx+A4h49pXPZvE3peXSUl5vmByVcfRVixo3lDTdEXZnRE6/fOgrpEuWGvYG2rMuNKjzc9SkBgoDqBDWO9JG+ZQkQkB6d3m0JQ5UFD0tNwcO+69ah1/Ll6LtuHc776ks2/P2UM4k9qXuZAm4SjAFZuVCcHoZVQ+LGjPPS2TlHUfAwKgq9V/4VGqs5yBqtFr3t5F0iIucIajWSbr0VAFD1zjsQrcplYVmhxQoh1nw17dAdTPjnSyd3dQ31lyQCdWcMnxtwieLdGnsv7PnqSBm+fWwyCk5WWywhqBL1OP4P1xN2OeKrOWrWSbnUKcqGZ3NOHZlzdulNsiS7TGB6OuKvmoGqt942vCFR9+gfvB1ixzudD/q+TRjqSvCQ/B8Te/ovRwE3Yw0swjLpn/H1J1el4KWeo713gk5wNnjIkYdE3pV4w2xUvPoq2o7/gsZduxA7caJpm9LphN057dBdTjX+T548if3790Or1WLsWD7MuK1BPpLk0uc6Oeq9AAy9FwUnqyWWJTMk7Drz0ELb4Wbu8OEcNal5dUKsg/HDnFNHMpxZepNsyS0TKKjViBoxQnoN3ocfxoW/vxsrTo7EC3kv2F2n2xsYPAwNTOzpv5QG3BoigTizx582DfDaTDVuvuMZvxmSy+AhkX9Rx8Uh4frrUf3eeyj/29+gq64xPZsonU7YXdMOPUFx4//999/H7bffjvb2dgiCgIsuughffPEFevDhRhljNv+GUiBWC/SbYPivEko/18nd3gvZhF3GBFauEEWfzFGTm1cnNphlDuOcOqJuJfdAa7sG7wY07tyJ1qNHAQBT+03t9oShksHD6Gj7X2LwMCAxsaf/UhpIe/vmFFS1VePC0yJu2iGiQwPcfFf3ryZkjsFDIv8X3r8/AKDlx/04++OjAAyjEgctfgLaaC3KmsoAvWHVoaQGQw6iw30EQKWCNlqLi1JGoHF3XkCM0lHc+F+6dCnmzp2LJ598EqdPn8Zjjz2GRYsW4c033/Tm+QUH62z+ABDXC0gb4uCLAhDfyxAocIInei+keudEvQ6n77jT4X7VSUnQWeUA0PTujbgpUxSdl6comleXmAhVRITF8oRMyEXkO+aBgYiBA1C0cyfqcnKQ9vhjCNNqoVZ13zrdssHDJrN8KgweBg0m9vRf0aMzoUm3MyWxM+D26iM52Fv5I8rrSyAWPoOYxiYMbUjv/hPuJBU8RKSDZzQGD4m6Vd3WrSj9y19s3u8oLUXxwmw889SdWHt0Lebl6pBqlhe9Ig5YdwVw+9DpKLpius10Rk+0JayDh54IKihu/P/666/IyclBv379MHDgQLz77rsYNWoUG/+OyGXzrz9r+DGRedS48gXAyV4tT/VeWPfOiTqdopvvuVtz0Lx3n2HIWlQkzi5ajI4zZ1Dz8cdImjPHqWtxh5J5dfqaGvR++22LZQv9OVpHFEoihwxB1OhMNO8pQPX77yNt4cJuOzaDh6HJmNhz6cZDFtPn0hMiseSaIUzs6SOC2s6URLOAmyYs3BAcTAd+m7AV9blfonHXLkQNH97t5ywXPESL2ahLBg+JfMruvb5zqfIer/4X2TW2yddT6oHsj3UQPn4T1gsBdpSWGsq/Gwk6pYKHnggqKM7239HRgSiztQ8HDx4MvV6PEgeNq5BmN5t/p+gUYM46IN7qgSK+l8vL/Bl7LwDLxDfmr13pvTDefA0vrL5rdsNShYebsnzHT5mCtAf+AAAoX7kKugYHC3V7kNJ5dbrKSmbzJ/JTyXNvAwDUrP8P9K2tdj8r6nRo3J2H2s83oXF3HkSd8yulGCkNHvZ84QVm8w8yV2b0xHdPXI737/4dVt08Eu/f/Tt898TlbPj7WPy0aei9aqXiDPgxEwyjJht37lK0f0/WH0qDh5q0NIv3mM2fqHs5vNeLIvQ1NRAg3aaSbUl1lv3S55e5VJcYg4fW52YMKtRt3er0Po2cSvi3bt06TJw4EcOHD0dsbCw0Gg2ammyXk6NODrP5A2iqNAQAFh60zQngxjxWb/VeyGbrttPblXTLLaj+YD3aiopQ8frr0D72mOz+3Rnewnl1RMEnbsrl0PTqiY6zxaj7/HMkzp4t+TlPR8idCR4mXH2V0/sn/8bEnv7JXsJQa8bGf9O+fdA3NkIVEyO7X0/XHxx5SBQYvLoEuSiio6QETXsKnErcqWQ0QunzyxA3ZYpL9YXixv/FF1+M5557DvX19VCpVBgwYABaWlrw5ptvYurUqcjMzER8fLzTJxDUnMnmr1I7tZyfEt5alsyZmy8ACGFh0C56AqfvXYCqd95F4uzZ6CivsPmuOzdfyaRcdm70hg9wXh2RvxM0GiT//vcoe3k5qt55FwnXXw/BauSR3PBaZ4bd2QQPkxk8JPJHSjPgh/Xti7DevdF+5gya9uxB7GWXSX7OG/WH+VQgexg8JPKt7riHOxtgUDIawZWggpHixv/27dsBAMeOHUNBQQEKCwtRUFCA119/HcuWLYNKpcKgQYNw+PBhp0+iu1133XXYtm0bpkyZgo8++shme1NTEy688ELMmTMHy5cvd/1AXsrm7wxv9V44u/xM7GWXIeaSS9C4YweKrrseotnwXYs1vl24+com5WpsNDthzqsjClSJN9yA8tf+jtajR9GUl2+Ti0RJhDx20iRTLhLrgCWTchEFH0EQEDNhAmo+/NCwdrdE498TPWxS9YdKYWcYg4dEvuUwmagHOFvOnVkO1BVODfsHgEGDBmHQoEG4+eabTe8VFRVhz5492Lt3r0sn0d0efPBB3HnnnVi3bp3k9r/85S8YN26c+wfqN8Ewd7+uGNLz/l3L5h+oYi+5GI07dlg0/AGgo6QEVW++Jf0lBzdfJuUiCn7qhAQkXDsTNR+sR2VnvW2+ComSCPnxyyZZrEJiHFUEgEm5iIJUzMSuxr8Ud3vY5Dof9HV19k+MwUMiv+AwmagoQpWYaFjq3IXggJJy3t0jD51u/EsZMGAABgwYgDndmMndHZMnT8a2bdsktx07dgxHjhzBNddcg4MHD7p3IJUauPLFzmz/nsvmH4hEnQ6Vb73t4pflb76cV0cUGpLnzkXNB+vR+PXXaPz6a9P7qgRlPWzWy492lJbizIMPQZWYyOAhUZCKHjcOEAS0HjuO9rIyhFkl2HOnh01J5wMABg+J/JyjfGYA7AYHbP5tJqx3b4iiiKbdeX4z8tAjjX9P2r59O15++WUUFBSguLgYGzZswKxZsyw+s3r1arz88ssoLi7G0KFDsXLlSlxyiWfmyz/66KN4+eWXsUsmSuy0ITMNWfu3PGGZ/C++l6Hh70I2/0CkpJHuiNTNl0m5iEJD6y+/SL6vr3XQwyan8yatr6mx+zEGD4kClyYpCZFDhqDlp5/Q9P33SLj2WsvtCnvOpD6n9LlGnZhoOeqIwUMiv+Mwn5mD4ID1NnVyMnQ1NWguLMSxcb+D3mwqsq9HHvpd47+xsREjRozAHXfcgdkSWZ3Xr1+PhQsXYvXq1Zg4cSLeeOMNZGVl4dChQ+jbty8AIDMzE60SS0Jt3boVvXr1kj32p59+ivPPPx/nn3++5xr/gKGBf8FVHs3mH2g8kU1T6ubrzo2biAKDqYfNRxg8JApcMRMmoOWnn9C4a5dN498031euEW+nh03pc03a4sUI02oZPCTyc/bymTkKDkhtK3nuOdS8/4FFwx/w/chDv2v8Z2VlISsrS3b7ihUrMH/+fNx1110AgJUrVyInJ8eUeBAACgoKXDr2Dz/8gA8++AAffvghGhoa0N7ejvj4eDz99NM2n21tbbUIMNQ5mt/lhWz+gcTdxrcmPV3y5hs9OhOatB7oKJO5CXNeHTngdFmmbueJkUPuYPAwMLAsk5SYiRNQ+c9/onHX9xBF0WK1EEGthnbxIkPvmxRRlO1hU1ovhGm1LmXkDlUsx+Sv7AUHrLeJOh0avtkmvSMfjzxUufXtbtbW1oaCggJMs4p2TJs2zSM99cuWLcPp06dx4sQJLF++HHfffbdkw9/42YSEBNNPnz593D5+MDNG1yE4WGZQZrvs8BaVCpr0nnb3xXl1ZA/Lsv9T2sOmSkiwfJ2U5N6BBUE28Ej+h2WZpESNGgUhMhId5eVoPXbMZrspCbHE80f02LGyPWzRozOhTk2VPzDrD5ewHFMw8FSnha6yEjHjxiLh6qsQM26sR9ozAdX4r6iogE6ng1ZruTSeVqtFiRP/g6dPn445c+Zg8+bNOOecc5Cfn+/0uSxevBi1tbWmn9OnTzu9j1BizKZpeGF1gxUEQBCQPP9OaLTSyx6qExIl36/buBEt+/cDKhXUKZZLGmq0WvRWsD4vhTaWZf+ntIet98qV6LtuHXotX46+69Zh0Lfb7AcdBcEw7K6zDrLeBjB4GEhYlkmKKjwc0aNHA4BN1n99WxvKV64CAKQ+9JCp/tAuMXT8NOXloXnfPtl9q+PipDew/nAZyzEFA09Mdwa8M/LQ74b9KyFYPaRZD+NyJCcnx+Fnbr/9drvbIyIiEBERofiY5DibZvy0aUjLzraYM1O76XPU/udDFP/v/2Lgp59AFRVl+l57SQlK/vwcAKDHHx9Ayj33yCfqIJLBsuz/HK7D2zm9J2bsGJsyb3cJHwA9n10KwDZZD5NyBR6WZZITM2ECGr/7Do27diHF7Pmu5v330X72LDRpaUiZd5vFM0bLgYOo/fhjlDz3F/T/z3oIKsv+sqq330ZbURGE8HCo4uOhq6gwbWP94TqWYwoGbjfavThtOaAa/6mpqVCr1Ta9/GVlZTajAcg/OUqYYT1nJnLoEDTu+A7tp06h7K8rETdlCjrKy6HukYrKf7wBfX09IocPR8rdd9udi0NEgcvhOryQ72FTEnQEpJP1MHhIFBxiJk4AADTl74G+rQ2q8HDo6utR8fo/AACpf3zAouEPAGnZD6N+61a0HDyI2g0bkGiWhLrl6M8oX/U3AED6kqeRMGsW6w8iMlHSaaFKSIC+ttbwuhuXAw2oxn94eDgyMzORm5uL6667zvR+bm4urrXK4Er+y5lGujo2Fj2fWYLT9y5A9TvvoPqddyw/oNGg1wsvQNAE1J8yETlJaSNe7ruOGvcMHhIFr4jzz4c6JQW6yko0792HmHFjUfnWW9DV1CB84EAkmj1TGmlSU5H6hz+g7MUXUbr8FaiTk6FvbII6KRGlL70Msb0dsZMnI+H66yEIAusPIjJR0mnhq5GHftdiamhowPHjx02vi4qKsG/fPiQnJ6Nv377Izs7G3LlzMXr0aIwfPx5r1qzBqVOnsGDBAh+eNXmTXmLZRpOODrQeP4aIgQO674SIyCeUNOLlsHFPFLoEQUDM+PGo+/xz1Hz0EVp/OY7KN98CAPR4eKFsB0Ly729B1dq16CgtxW/33W+xTRUdjZ7PLnVq2ikRhQ5/HXnod43/PXv2YPLkyabX2dnZAIB58+Zh7dq1uOmmm1BZWYlnn30WxcXFyMjIwObNm9GvXz9fnTJ5kcP1vQUBpc8vQ9yUKRxiRxQC2IgnIleo4uMBGBIF123caHgzLAzQy6+zXb9tm8Ua2+b0TU1o2ruX8/qJSJY/jjz0u8b/pEmTIErNjTBz//334/7777f7GQoODpfKEEV0lJSgaU8BGwRERERko27rVtT8+9+2G9rbcWbhQkBiZSB2PhCRJ/hbp0VALfVHoUfpUhmeWlKDiIiIgofDRjwMc25Fnc7iPWc6H4iIAgUb/+TXlC6V4Y11MImIiCiwudqIZ+cDEQUjNv7JrxmXyoBcQh1BgCY93SvrYBIREVFgc7URz84HIgpGbPyTXzMulWF4YRUA8PI6mERERBTYXG3Es/OBiIIRG//k9+KnTUPvVSuh0Wot3tdotegtkaSHiIiICHC9Ec/OByIKRn6X7Z9IijvrexMREVFoMjbizzy00NBoN19RykEjXuk63UREgYKNfwoY/rZUBhEREfk/dxrx7HwgomDCxj8RERERBTV3GvHsfCCiYMHGPxEREREFPTbiiSjUMeEfERERERERUZBj45+IiIiIiIgoyLHxT0RERERERBTk2PgnIiIiIiIiCnJs/IeI745VYOqKb/HdsQrnv/zLN8BrYw3/dcH3Z7/HtZ9ci+/Pfu/0dxt37cIvV12Nxl27XDo2EXmGW3UI4FY9wjqEKDj46lnEnToEYD1C5C9Yh7iPjf8QIIoiXso5guNlDXgp5whEUXTmy8BXS4GKo4b/OvPdzmOvKlyFX2t/xarCVU4dWxRFlK34K9p++QVlK/7q3HkTkce4VYcYduByPcI6hCg4+OpZxJ06xPh91iNEvsc6xDPY+A8B249VYP9vtQCA/b/VYrsz0bJfvgLO7jX8++xew2sn7Dq7Cz9V/gQA+KnyJ+w6qzzi1fjdTrQcPAgAaDl4EI3f7XTq2ETkGW7VIYBb9QjrEKLg4KtnEXfqEID1CJG/YB3iGWz8BzlRFPHK1qNQCYbXKgF4ZetRZVEnUQS+fg4Q1IbXgtrwWmHEShRFvLr3VagEVeexVXh176uKji2KIspXrQJUnX+iKhXKVzkfbSMi97hVhxh24HI9wjqEKDj46lnEnTrE+H3WI0S+xzrEc9j4D3LGKJm+829MLzoRLTNGyUSd4bWocypaZoyU6UV957H1iiNmpiiZXt954nq/iJYRhRq36hDArXqEdQhRcPDVs4g7dQjAeoTIX7AO8Rw2/oOYdZTMSFG0zDpKZqQwWmYdKes6tuOImU2UzPRl30fLiEKJW3WIYQcu1yOsQ4iCg6+eRdypQ4zfZz1C5HusQzyLjf8gZh0lM1IULbOOkhkpjJZZR8q6ju04YmYTJTN92ffRMqJQ4lYdArhVj7AOIQoOvnoWcacOAViPEPkL1iGexcZ/kDJGyQRBertgL1pmjJLJ/nmo7EbLjJEyAdIHFyDIRsxMUTI7J86IO5H3uVWHGHbgcj3COoQoOPjqWcSdOsT4fdYjRL7HOsTz2PgPUm06Pc7WNMuOZhFFoLimBW06ve1GXRtQewaAxDbA8H7dGcPnJLTr21HSWAIRMgUCIkoaS9Cub7fd1t6O9uJi+WE4ooj2khKI7bbfJSLPcasOAdyqR1iHEAUHXz2LuFOHAKxHiPwF6xDPE0SGLT2irq4OCQkJqK2tRXx8vK9PBwBwtqYZVY3SDXQASIkNR8+EKOmNtb8BjXaG0cT0ABJ6y24uaSxBVUuV7PbkyGSkx6RLbmsvLkZHlfx3NSkpCEuX/i75N38sJ9YC4Ry7i1t1COBWPcI6xL8FQjkJhHMMBb56FnGnDgFCpx7x93Li7+dH3sc6xDFnyklINv6vu+46bNu2DVOmTMFHH31kev/o0aO46aabLF6///77mDVrlsN9snIiciwQykkgnCORrwVCOQmEcyTyNX8vJ/5+fkT+wJlyEpLD/h988EG88847Nu8PHjwY+/btw759+/Ddd98hJiYGV1xxhQ/OkIiIiIiIiMhzQrLxP3nyZMTFxdn9zGeffYYpU6YgJiamm86KiIiIiIiIyDv8rvG/fft2XHPNNejVqxcEQcAnn3xi85nVq1djwIABiIyMRGZmJnbs2OHx8/jPf/5jMQWAiIiIiIiIKFD5XeO/sbERI0aMwGuvvSa5ff369Vi4cCH+9Kc/Ye/evbjkkkuQlZWFU6dOmT6TmZmJjIwMm5+zZ88qOoe6ujrs3LkTM2bM8Mg1EREREREREfmSxtcnYC0rKwtZWVmy21esWIH58+fjrrvuAgCsXLkSOTk5eP3117Fs2TIAQEFBgVvn8Omnn2L69OmIjIyU/UxraytaW1tNr+vq6tw6JhH5BssyUXBgWSYKfCzHRN7ldz3/9rS1taGgoADTpk2zeH/atGnYtWuXx46jZMj/smXLkJCQYPrp06ePx45PRN2HZZkoOLAsEwU+lmMi7wqoxn9FRQV0Oh20Wq3F+1qtFiUlJYr3M336dMyZMwebN2/GOeecg/z8fNO22tpa5OXlYfr06Xb3sXjxYtTW1pp+Tp8+7dzFEJFfYFkmCg4sy0SBj+WYyLv8bti/EoIgWLwWRdHmPXtycnJktyUkJKC0tNThPiIiIhAREaH4mETkn1iWiYIDyzJR4GM5JvKugOr5T01NhVqttunlLysrsxkNQEREREREREQGAdX4Dw8PR2ZmJnJzcy3ez83NxYQJE3x0VkRERERERET+ze+G/Tc0NOD48eOm10VFRdi3bx+Sk5PRt29fZGdnY+7cuRg9ejTGjx+PNWvW4NSpU1iwYIEPz5qIiIiIiIjIf/ld43/Pnj2YPHmy6XV2djYAYN68eVi7di1uuukmVFZW4tlnn0VxcTEyMjKwefNm9OvXz1enTEREREREROTX/K7xP2nSJIiiaPcz999/P+6///5uOiMiIiIiIiKiwBZQc/6JiIiIiIiIyHls/BMREREREREFOTb+iYiIiIiIiIIcG/9EREREREREQY6NfyIiIiIiIqIgx8Y/ERERERERUZBj45+IiIiIiIgoyLHxT0RERERERBTk2PgnIiIiIiIiCnJs/BMREREREREFOTb+iYiIiIiIiIIcG/9EREREREREQY6NfyIiIiIiIqIgx8Y/ERERERERUZBj45+IiIiIiIgoyLHxT0RERERERBTk2PgnIiIiIiIiCnJs/BMREREREREFOTb+iYiIiIiIiIIcG/9EREREREREQY6NfyIiIiIiIqIgx8Y/ERERERERUZBj45+IiIiIiIgoyIVc4//06dOYNGkShgwZguHDh+PDDz+02P75559j8ODBGDRoEP71r3/56CyJiIiIiIiIPEfj6xPobhqNBitXrsTIkSNRVlaGUaNGYcaMGYiJiUFHRweys7PxzTffID4+HqNGjcL111+P5ORkX582ERERERERkctCrue/Z8+eGDlyJAAgLS0NycnJqKqqAgDk5eVh6NCh6N27N+Li4jBjxgzk5OT48GyJiIiIiIiI3Od3jf/t27fjmmuuQa9evSAIAj755BObz6xevRoDBgxAZGQkMjMzsWPHDpeOtWfPHuj1evTp0wcAcPbsWfTu3du0/ZxzzsGZM2dc2jcRERERERGRv/C7xn9jYyNGjBiB1157TXL7+vXrsXDhQvzpT3/C3r17cckllyArKwunTp0yfSYzMxMZGRk2P2fPnjV9prKyErfddhvWrFljek8URZvjCYLgwasjIiIiIiIi6n5+N+c/KysLWVlZsttXrFiB+fPn46677gIArFy5Ejk5OXj99dexbNkyAEBBQYHdY7S2tuK6667D4sWLMWHCBNP7vXv3tujp/+233zBu3DjZfbS2tppe19bWAgDq6uocXCFR6DKWD6lAm6+wLBM5j2WZKDj4W1lmOSZynlPlWPRjAMQNGzaYXre2topqtVr8+OOPLT734IMPipdeeqmifer1evHmm28WlyxZYrOtvb1dPO+888TffvtNrKurE8877zyxoqJCcj9LliwRAfCHP/xx4ef06dOK6wFvY1nmD39c/2FZ5g9/guPHX8oyyzF/+OP6j5JyLIiin4T6JAiCgA0bNmDWrFkAuubk79y506LH/vnnn8e6detw9OhRh/v87rvvcOmll2L48OGm9959910MGzYMAPDZZ5/h0UcfhV6vx+OPP4577rlHcj/WkUm9Xo+qqiqkpKQE3VSBuro69OnTB6dPn0Z8fLyvT6fbhOJ1e/uaRVFEfX09evXqBZXKP2YdsSwHt1C8ZoBlGWBZDja8Zu9cs7+VZZbj4BeK1+1P92S/G/avhHXhF0VRcYVw8cUXQ6/Xy26fOXMmZs6c6XA/ERERiIiIsHgvMTFR0TkEqvj4+JAppOZC8bq9ec0JCQle2a+rWJZDQyheM8CyzLIcfHjNnudPZZnlOHSE4nX7wz3Z9yE+J6SmpkKtVqOkpMTi/bKyMmi1Wh+dFREREREREZF/C6jGf3h4ODIzM5Gbm2vxfm5ursU0ACIiIiIiIiLq4nfD/hsaGnD8+HHT66KiIuzbtw/Jycno27cvsrOzMXfuXIwePRrjx4/HmjVrcOrUKSxYsMCHZx3cIiIisGTJEpthWMEuFK87FK85lITi7zcUrxkI3esOFaH4++U1U7AJ1d9vKF63P12z3yX827ZtGyZPnmzz/rx587B27VoAwOrVq/HSSy+huLgYGRkZ+Otf/4pLL720m8+UiIiIiIiIKDD4XeOfiIiIiIiIiDwroOb8ExEREREREZHz2PgnIiIiIiIiCnJs/BMREREREREFOTb+iYiIiIiIiIIcG//kccuXL8fQoUORkZGB9957z9en0y00Gg1GjhyJkSNH4q677vL16XSL6667DklJSbjhhht8fSrkBaFYjgGWZQo+oViWQ7EcAyzLwY5lOTTKsrfLMbP9k0cdOHAA8+bNw65duwAAU6ZMwaZNm5CYmOjbE/Oy1NRUVFRU+Po0utU333yDhoYGrFu3Dh999JGvT4c8KFTLMcCyzLIcXEK1LIdiOQZYloMZy3Lo8HY5Zs8/edThw4cxYcIEREZGIjIyEiNHjsSWLVt8fVrkBZMnT0ZcXJyvT4O8gOU4tLAsBy+W5dDCshy8WJZDh7fLMRv/IWb79u245ppr0KtXLwiCgE8++cTmM6tXr8aAAQMQGRmJzMxM7NixQ/H+MzIy8M0336CmpgY1NTX4+uuvcebMGQ9egfO8fc0AUFdXh8zMTFx88cX49ttvPXTmruuOaybfCcVyDLAssywHn1Asy6FYjgGW5WDHshwaZTkYyrHG1ydA3auxsREjRozAHXfcgdmzZ9tsX79+PRYuXIjVq1dj4sSJeOONN5CVlYVDhw6hb9++AIDMzEy0trbafHfr1q0YMmQIHnzwQVx++eVISEjAmDFjoNH49s/M29fcq1cvnDhxAr169cLBgwdx1VVX4cCBA4iPj/f6tcnpjmsm3wnFcgywLLMsB59QLMuhWI4BluVgx7IcGmU5KMqxSCELgLhhwwaL98aOHSsuWLDA4r0LLrhAXLRokUvHmD9/vvj555+7eooe1x3XfOWVV4r5+fmunqLHefOav/nmG3H27NnuniK5IRTLsSiyLBuxLAePUCzLoViORZFlOdixLBsEe1kO1HLMYf9k0tbWhoKCAkybNs3i/WnTppkSjChRVlYGADh69Cjy8vIwffp0j56nJ3nimqurq00RvN9++w2HDh3CwIEDPX6unuKp3zP5p1AsxwDLsjmW5eAQimU5FMsxwLIc7FiWuwRzWQ6Ucuz7cZzkNyoqKqDT6aDVai3e12q1KCkpUbyfWbNmoaamBjExMXj77bd9PizJHk9c8+HDh3HvvfdCpVJBEASsWrUKycnJ3jhdj/DU73n69OkoLCxEY2MjzjnnHGzYsAFjxozx9OmSk0KxHAMsy+ZYloNDKJblUCzHAMtysGNZ7hLMZTlQyrH//tWQzwiCYPFaFEWb9+zxp+iWUu5c84QJE3DgwAFvnJZXuft7zsnJ8fQpkQeFYjkGWJYBluVgE4plORTLMcCyHOxYlkOjLPt7OeawfzJJTU2FWq22iU6VlZXZRLGCBa+5SzBfcygJ1d9vKF53KF5zKAnF328oXjMQutcdKkLx98tr7uJv18zGP5mEh4cjMzMTubm5Fu/n5uZiwoQJPjor7+I1dwnmaw4lofr7DcXrDsVrDiWh+PsNxWsGQve6Q0Uo/n55zV387Zo57D/ENDQ04Pjx46bXRUVF2LdvH5KTk9G3b19kZ2dj7ty5GD16NMaPH481a9bg1KlTWLBggQ/P2j285tC45lASqr/fULzuULzmUBKKv99QvGYgdK87VITi75fXHKDX7JU1BMhvffPNNyIAm5958+aZPvP3v/9d7NevnxgeHi6OGjVK/Pbbb313wh7Aaw6Naw4lofr7DcXrDsVrDiWh+PsNxWsWxdC97lARir9fXnNgXrMgiqLomTACEREREREREfkjzvknIiIiIiIiCnJs/BMREREREREFOTb+iYiIiIiIiIIcG/9EREREREREQY6NfyIiIiIiIqIgx8Y/ERERERERUZBj45+IiIiIiIgoyLHxT0RERERERBTk2PgnIiIiIiIiCnJs/BMREREREREFOTb+icxMmjQJgiBAEATs27fPa8e5/fbbTcf55JNPvHYcolDFskwUHFiWiQIfy7H/YOOfyMrdd9+N4uJiZGRkeO0Yq1atQnFxsdf2T0Qsy0TBgmWZKPCxHPsHja9PgMjfREdHIz093avHSEhIQEJCglePQRTqWJaJggPLMlHgYzn2D+z5J5fNnDnTNLTG+uezzz4LmuNOmjQJf/zjH7Fw4UIkJSVBq9VizZo1aGxsxB133IG4uDice+65+OKLLyy+99FHH2HYsGGIiopCSkoKpk6disbGRo+fH5G7WJZZlik4sCyzLFPgYzlmOfYmNv7JZW+//TaKi4tx7NgxAMDmzZtRXFyM4uJizJgxI6iOu27dOqSmpiIvLw9//OMfcd9992HOnDmYMGECCgsLMX36dMydOxdNTU0AgOLiYvzP//wP7rzzThw+fBjbtm3D9ddfD1EUvXJ+RO5gWWZZpuDAssyyTIGP5Zjl2KtEIjft2rVLFARBrKurC/jjXnbZZeJDDz1k897FF19set3R0SHGxMSIc+fONb1XXFwsAhC///57URRFsaCgQAQgnjhxwu7xAIgbNmzw2PkTuYNlmWWZggPLMssyBT6WY5Zjb2DPP7lt//796N+/P+Li4pz63jPPPCM7vMj4s2fPHo8f1xXDhw83/VutViMlJQXDhg0zvafVagEAZWVlAIARI0ZgypQpGDZsGObMmYN//vOfqK6u9vp5ErmDZZllmYIDyzLLMgU+lmOWY29g45/ctn//fovCa/TGG29g1KhRyMjIwC233GKz/YEHHsDhw4ft/tjLCCp3XADIyspCdnY2fve73+GCCy5Afn4+Zs6ciX79+mHNmjVOX2NYWJjFa0EQLN4TBAEAoNfrARgqsNzcXHzxxRcYMmQIXn31VQwePBhFRUVOH5uou7AssyxTcGBZZlmmwMdyzHLsDcz2T247ceKETSVSXV2NNWvWID8/H2q1GjU1NTbfS01NRWpqqkePa3Tw4EHcdNNNWLFiBW677TY88cQT2LhxI44dO4b77rsP99xzj8vHVUoQBEycOBETJ07E008/jX79+mHDhg3Izs72+rGJXMGyLI1lmQINy7I0lmUKJCzH0liO3cOef3KbXq/HyZMn8dtvv5kSbmg0GlRWVuKJJ57ATz/9hMTExG45LgDU1tYiPDwct99+OwAgMjISDz30EGJiYhAREdEtS4Ds3r0bzz//PPbs2YNTp07h448/Rnl5OS688EKvH5vIVSzLtliWKRCxLNtiWaZAw3Jsi+XYfWz8k9sefPBB7Ny5ExdccIGpkoiLi8OBAwcwYsQI3HDDDfj888+75biAISo5ZswY0+sDBw5g3Lhxpn/bG+rkKfHx8di+fTtmzJiB888/H0899RReeeUVZGVlef3YRK5iWbbFskyBiGXZFssyBRqWY1ssx+7jsH9yW1ZWFk6fPm3x3rFjxzBo0CDMnTsXO3bsQGtra7ccFzBUTsZkIaIoorS0FOnp6TbblNq2bZvNeydOnLB5z7yCvPDCC7FlyxanjkPkayzLMB3LiGWZAhHLMkzHMmJZpkDDcgzTsYxYjt3Hnn/yij//+c8YPHgwLrroIkRGRuK6667rtmP/9NNPpgroxIkT6N+/v2mbkspp9erViI2NxYEDB7x2jgsWLEBsbKzX9k/kKSzL9rEsU6BgWbaPZZkCAcuxfSzHjgmieTiFKMSdOXMGzc3NAIC+ffsiPDzcK8cpKytDXV0dAKBnz56IiYnxynGIQhXLMlFwYFkmCnwsx/6DjX8iIiIiIiKiIMdh/0RERERERERBjo1/IiIiIiIioiDHxj8RERERERFRkGPjn4iIiIiIiCjIsfFPREREREREFOTY+CciIiIiIiIKcmz8ExEREREREQU5Nv6JiIiIiIiIghwb/0RERERERERBjo1/IiIiIiIioiD3/50pU28RY75HAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1200x300 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "h = np.array([[1, 0.1, 0.01, 0.001]]).T\n",
    "tau_ms = [0.1, 1, 10, 100]\n",
    "delta_tau = np.logspace(-12, 0, 26)\n",
    "\n",
    "fig = plt.figure(figsize=(12, 3))\n",
    "for ix, tau_m in enumerate(tau_ms):\n",
    "    tau_s = tau_m + delta_tau\n",
    "    p31, p31s, _, _ = calc_p(tau_m, tau_s, h)\n",
    "\n",
    "    ax = fig.add_subplot(1, len(tau_ms), ix + 1)\n",
    "    l = ax.loglog(np.abs(tau_s - tau_m), np.abs(p31 - p31s).T, \"o-\", label=[f\"h = {hv:.3f} ms\" for hv in h[:, 0]])\n",
    "    ax.set_prop_cycle(None)\n",
    "    for hv in h[:, 0]:\n",
    "        ax.loglog(1e-8 * tau_m**2 / hv, 1e-16, \"^\")\n",
    "    ax.set_ylim([1e-20, 5e-2])\n",
    "    ax.set_xlabel(r\"$\\tau_s - \\tau_m$ [ms]\")\n",
    "    ax.set_title(f\"$\\\\tau_m = {tau_m}$ ms\")\n",
    "    if ix == 0:\n",
    "        ax.set_ylabel(\"$P - P_{singular}$\")\n",
    "        plt.legend(loc=\"upper left\")\n",
    "    else:\n",
    "        ax.set_yticklabels([]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- The point at which numerical instability occurs clearly depends on the membrane time constant\n",
    "- As indicated by the markers, the breakdown point is located roughly at $$\\tau_s - \\tau_m < 10^{-8}\\times\\frac{\\tau_m^2}{h}$$\n",
    "- We can thus use $$(\\tau_s - \\tau_m)h < 10^{-8}\\times \\tau_m^2$$ or \n",
    "  $$h < 10^{-8}\\times\\frac{\\tau_m^2}{|\\tau_s - \\tau_m|}$$ as criterium: use $P_{s, 31}$ if this condition is fulfilled.\n",
    "- To ensure some margin of safety, we can set the limit at $10^{-7}\\times\\tau_m^2$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algorithm for propagator computing\n",
    "\n",
    "1. Precompute values that can be precomputed independent of $h$, including useful inverses.\n",
    "2. Compute $P_{32}$, which will always be stable; replace by singular limit only if a numerically non-normal or non-positive result occurs. \n",
    "3. If $h$ is below stability limit (see inequality above), use singular $P_{s, 31}$, otherwise use $P_{31}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exploration\n",
    "We will now show that the stability criterion explained above leads to a reasonable behavior for $\\tau_s\\rightarrow\\tau_m$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simulation\n",
    "\n",
    "- Create one neuron for each value of `delta_tau`\n",
    "- Drive neurons with a single spike\n",
    "- Measure resulting membrane potential"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "tau_m = 10.0\n",
    "h = 0.1\n",
    "delta_tau = np.hstack(([0.0], np.logspace(-10, -1, 10)))\n",
    "\n",
    "nest.ResetKernel()\n",
    "nest.resolution = h\n",
    "\n",
    "neurons = nest.Create(\"iaf_psc_alpha\", n=len(delta_tau), params={\"tau_m\": tau_m, \"tau_syn_ex\": tau_m + delta_tau})\n",
    "spike_gen = nest.Create(\"spike_generator\", params={\"spike_times\": [1.0]})\n",
    "vm = nest.Create(\"voltmeter\", params={\"interval\": h})\n",
    "\n",
    "nest.Connect(spike_gen, neurons, syn_spec={\"weight\": 100.0})\n",
    "nest.Connect(vm, neurons)\n",
    "\n",
    "nest.Simulate(10 * tau_m)\n",
    "\n",
    "v = pd.DataFrame.from_records(vm.events).set_index(\"times\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "v.groupby(\"senders\").V_m.plot(alpha=0.5, figsize=(8, 3))\n",
    "plt.legend(delta_tau)\n",
    "plt.xlabel(\"Time [ms]\")\n",
    "plt.ylabel(\"Membrane voltage [mV]\")\n",
    "plt.title(\"Response to single input spike for different tau_m - tau_s\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Maximum of membrane potential"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x300 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "V_max = v.groupby(\"senders\").V_m.max()\n",
    "plt.figure(figsize=(10, 3))\n",
    "plt.subplot(1, 3, 1)\n",
    "plt.semilogx([1e-10, 1], [V_max.iloc[0], V_max.iloc[0]], \"--\")\n",
    "plt.semilogx(delta_tau[1:], V_max.iloc[1:], \"o-\", alpha=0.6)\n",
    "plt.legend((\"Singular limit\", \"$tau_s > tau_m$\"))\n",
    "plt.xlabel(r\"$\\tau_s - \\tau_m$\")\n",
    "plt.ylabel(\"$V_{max} [mV]$\")\n",
    "\n",
    "plt.subplot(1, 3, 3)\n",
    "plt.loglog(delta_tau[1:], V_max.iloc[1:] - V_max.iloc[0], \"o-\")\n",
    "plt.xlabel(r\"$\\tau_s - \\tau_m$\")\n",
    "plt.ylabel(\"$V_{max} - V_{max}^{singular} [mV]$\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The maximum membrane potential converges smoothly against the singular limit, indicating that no numerical instabilities occur."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "-----------------------------\n",
    "### License\n",
    "\n",
    "This file is part of NEST. Copyright (C) 2004 The NEST Initiative\n",
    "\n",
    "NEST is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 2 of the License, or (at your option) any later version.\n",
    "\n",
    "NEST is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details."
   ]
  }
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